Middle School Math Quiz: Solve One Step Equations
20 questions · exam conditions
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Solve One Step EquationsQuestion 1 of 20

Ava had some money. She earned $15 more, and now she has $42. Write an equation of the form $x+p=qandsolveforand solve forx$. What was Ava's starting amount?

x=27x=27 dollars
x=25x=25 dollars
x=57x=57 dollars
x=42x=42 dollars
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Middle School Math Quiz

Middle School Math Quiz: Solve One Step Equations

Practice Solve One Step Equations in Middle School Math with focused quiz questions that help you check what you know, review explanations, and build confidence with test-style prompts.

What this quiz covers

This quiz focuses on Solve One Step Equations, giving you a quick way to practice the rules, question types, and explanations that matter most for Middle School Math.

How to use this quiz

Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

All questions

Question 1

Ava had some money. She earned $15 more, and now she has $42. Write an equation of the form $x+p=qandsolveforand solve forx$. What was Ava's starting amount?

  1. x=27x=27 dollars (correct answer)
  2. x=25x=25 dollars
  3. x=57x=57 dollars
  4. x=42x=42 dollars
Explanation: This question tests writing and solving one-step equations of the form x + p = q from real-world problems with nonnegative rational numbers, using inverse operations. One-step equations in addition form x + p = q are solved by subtracting p from both sides to get x = q - p; for example, if x + 15 = 42, then x = 42 - 15 = 27, and for multiplication form p x = q, solve by dividing both sides by p to get x = q / p, like 6x = 18 gives x = 18 ÷ 6 = 3. Inverse operations undo the original operation: addition is undone by subtraction, and multiplication by division, with nonnegative rational numbers including whole numbers like x=27, p=15, q=42, fractions such as x=1/2 from x + 1/4 = 3/4, or decimals like x=4 from 2.5x=10, all greater than or equal to zero. For example, if Maria has x dollars, earns $15, and now has $42, the equation is x + 15 = 42, solved by subtracting 15 to get x = 27, meaning she started with $27; or for 6 items at $x each totaling $18, it's 6x = 18, divided by 6 to get x = 3, so each costs $3; or with fractions, x + 1/4 = 3/4 gives x = 3/4 - 1/4 = 1/2 cup. In this case, the correct equation is x + 15 = 42, solved as x = 42 - 15 = 27, so Ava started with $27. Common errors include using the wrong operation like adding instead of subtracting to get x = 42 + 15 = 57, or arithmetic mistakes like 42 - 15 = 25, or setting up the equation incorrectly as x - 15 = 42. To solve, (1) write the equation from the context where 'earned $15 more' means add 15, (2) identify the addition form, (3) apply subtraction as the inverse, (4) calculate 42 - 15 = 27, (5) verify by substituting 27 + 15 = 42, and (6) interpret as starting amount of $27; remember all values are nonnegative, and avoid mistakes like wrong operations or not verifying the solution.

Question 2

A runner ran 2.52.5 miles each day for xx days and ran 1515 miles total. Write and solve a one-step equation to find xx.

  1. Equation: 2.5x=152.5x=15; solution: x=5x=5 (correct answer)
  2. Equation: 2.5x=152.5x=15; solution: x=6x=6
  3. Equation: 2.5x=152.5x=15; solution: x=37.5x=37.5
  4. Equation: x+2.5=15x+2.5=15; solution: x=12.5x=12.5
Explanation: This question tests writing and solving one-step equations of the form x + p = q or p x = q from real-world problems involving nonnegative rational numbers, using inverse operations to solve. One-step equations include the addition form x + p = q solved by subtracting p from both sides to get x = q - p, for example, if x + 15 = 42, then x = 42 - 15 = 27; or the multiplication form p x = q solved by dividing both sides by p to get x = q / p, for example, if 6x = 18, then x = 18 ÷ 6 = 3; inverse operations undo the original operation, so addition is undone by subtraction and multiplication by division, with nonnegative rational numbers like whole numbers (x=27, p=15, q=42), fractions (x=1/2 from x + 1/4 = 3/4), or decimals (x=4 from 2.5x = 10), all greater than or equal to zero. For example, Maria has x dollars, earns $15, and now has $42, so the equation is x + 15 = 42, solved by subtracting 15 to get x = 27, meaning she started with $27; or for 6 items at $x each totaling $18, the equation is 6x = 18, solved by dividing by 6 to get x = 3, so each costs $3; or with fractions, x + 1/4 = 3/4, solved as x = 3/4 - 1/4 = 1/2 cup. In this problem, the correct equation is 2.5x = 15, solved by dividing by 2.5 to get x = 6, meaning the runner ran for 6 days. A common error is setting up addition instead like choice B, or dividing wrong like choice C (15 × 2.5 = 37.5) or choice D (perhaps 15 - 10 or miscalculation). To solve these problems: (1) write the equation from the context, identifying the operation such as 'each day' meaning multiplication, (2) identify the form as x + p = q or p x = q, (3) apply the inverse operation like subtracting p or dividing by p, (4) calculate accurately, such as 15 ÷ 2.5 = 6, (5) verify by substituting back, like 2.5 × 6 = 15, and (6) interpret the solution in context, such as x = 6 means 6 days. Remember, all values are nonnegative, including whole numbers, fractions, or decimals greater than or equal to zero, and avoid mistakes like using addition instead of multiplication, decimal division errors, or failing to verify.

Question 3

At a school book fair, Jada had some money. After she earned $12.50 helping a teacher, she had $30.00 total. Write an equation of the form $x+p=qandsolveforand solve forx$. What was her starting amount of money?

  1. Equation: x+12.50=30.00x+12.50=30.00; x=17.50x=17.50 dollars (correct answer)
  2. Equation: x+12.50=30.00x+12.50=30.00; x=42.50x=42.50 dollars
  3. Equation: x+12.50=30.00x+12.50=30.00; x=12.50x=12.50 dollars
  4. Equation: x−12.50=30.00x-12.50=30.00; x=42.50x=42.50 dollars
Explanation: This question tests writing and solving one-step equations of the form x + p = q from real-world problems with nonnegative rational numbers, using inverse operations. One-step equations in addition form x + p = q are solved by subtracting p from both sides to get x = q - p; for example, if x + 15 = 42, then x = 42 - 15 = 27, and inverse operations undo the original by subtracting for addition, with nonnegative rationals like decimals such as x = 4 from 2.5x = 10, all values ≥0. For instance, if Maria has x dollars and earns $15 to reach $42, the equation is x + 15 = 42, solved by x = 42 - 15 = 27, meaning she started with $27; similarly, for fractions, x + 1/4 = 3/4 gives x = 1/2 cup. In this problem, Jada's starting amount x plus $12.50 earned equals $30.00, so the correct equation is x + 12.50 = 30.00, and solving gives x = 30.00 - 12.50 = 17.50 dollars. Common errors include using subtraction instead of addition like x - 12.50 = 30.00 leading to x = 42.50, or arithmetic mistakes like x = 30.00 + 12.50 = 42.50 or x = 12.50. To solve, (1) write the equation from context where 'earned $12.50' means addition, (2) identify the form x + p = q, (3) apply inverse by subtracting p, (4) calculate 30.00 - 12.50 = 17.50, (5) verify 17.50 + 12.50 = 30.00, and (6) interpret as starting with $17.50. Remember, all values are nonnegative, avoiding negatives, and mistakes often involve wrong setup or not verifying the solution.

Question 4

A class collected 18 cans for a food drive. Each student brought the same number of cans. If 6 students participated, let xx be the number of cans each student brought. Solve the equation 6x=186x=18.

  1. x=18−6=12x=18-6=12
  2. x=18÷6=3x=18\div 6=3 (correct answer)
  3. x=6÷18=13x=6\div 18=\tfrac{1}{3}
  4. x=6+18=24x=6+18=24
Explanation: This question tests solving one-step equations of the form px = q from real-world problems with nonnegative rational numbers, using inverse operations. One-step equations in multiplication form px = q are solved by dividing both sides by p to get x = q / p; for example, if 6x = 18, then x = 18 ÷ 6 = 3, and inverse operations undo the original by dividing for multiplication, with nonnegative rationals like whole numbers such as x = 27 from x + 15 = 42 but here multiplication, all values ≥0. For instance, if 6 students bring x cans each for 18 total, the equation is 6x = 18, solved by x = 18 ÷ 6 = 3, meaning each brought 3; similarly, for decimals, 2.5x = 10 gives x = 4. In this problem, the correct solution for 6x = 18 is x = 18 ÷ 6 = 3. Common errors include subtracting like x = 18 - 6 = 12, adding x = 6 + 18 = 24, or reversing division x = 6 ÷ 18 = 1/3. To solve, (1) identify the form px = q from the given equation, (2) apply inverse by dividing by p, (3) calculate 18 ÷ 6 = 3, (4) verify 6 × 3 = 18, and (5) interpret as 3 cans each. Remember, all values are nonnegative whole numbers, and mistakes often involve using the wrong operation or arithmetic errors in division.

Question 5

Solve the one-step equation x+0.4=3.1x+0.4=3.1 and interpret what xx represents as the starting amount before adding 0.40.4.

  1. x=2.7x=2.7; the starting amount was 2.72.7 (correct answer)
  2. x=3.5x=3.5; the starting amount was 3.53.5
  3. x=1.24x=1.24; the starting amount was 1.241.24
  4. x=0.4x=0.4; the starting amount was 0.40.4
Explanation: This question tests writing and solving one-step equations of the form x + p = q or p x = q from real-world problems involving nonnegative rational numbers, using inverse operations to solve. One-step equations include the addition form x + p = q solved by subtracting p from both sides to get x = q - p, for example, if x + 15 = 42, then x = 42 - 15 = 27; or the multiplication form p x = q solved by dividing both sides by p to get x = q / p, for example, if 6x = 18, then x = 18 ÷ 6 = 3; inverse operations undo the original operation, so addition is undone by subtraction and multiplication by division, with nonnegative rational numbers like whole numbers (x=27, p=15, q=42), fractions (x=1/2 from x + 1/4 = 3/4), or decimals (x=4 from 2.5x = 10), all greater than or equal to zero. For example, Maria has x dollars, earns $15, and now has $42, so the equation is x + 15 = 42, solved by subtracting 15 to get x = 27, meaning she started with $27; or for 6 items at $x each totaling $18, the equation is 6x = 18, solved by dividing by 6 to get x = 3, so each costs $3; or with fractions, x + 1/4 = 3/4, solved as x = 3/4 - 1/4 = 1/2 cup. In this problem, the correct solution is x = 2.7, solved by subtracting 0.4 from 3.1, meaning the starting amount was 2.7 before adding 0.4. A common error is adding instead like choice B (3.1 + 0.4 = 3.5), or subtracting wrong like choice C (perhaps 3.1 - 1.86 or miscalculation) or choice D (maybe confusing with division). To solve these problems: (1) write the equation from the context, identifying the operation such as 'adding 0.4' meaning addition, (2) identify the form as x + p = q or p x = q, (3) apply the inverse operation like subtracting p or dividing by p, (4) calculate accurately, such as 3.1 - 0.4 = 2.7, (5) verify by substituting back, like 2.7 + 0.4 = 3.1, and (6) interpret the solution in context, such as x = 2.7 means starting amount of 2.7. Remember, all values are nonnegative, including whole numbers, fractions, or decimals greater than or equal to zero, and avoid mistakes like using addition instead of subtraction, decimal errors, or not verifying.

Question 6

A recipe needs a total of 34\tfrac{3}{4} cup of milk. You already poured in 14\tfrac{1}{4} cup. Let xx be the amount of milk still needed. Write an equation and solve it.

  1. Equation: x+14=34x+\tfrac{1}{4}=\tfrac{3}{4}; x=1x=1 cup
  2. Equation: x+14=34x+\tfrac{1}{4}=\tfrac{3}{4}; x=12x=\tfrac{1}{2} cup (correct answer)
  3. Equation: x−14=34x-\tfrac{1}{4}=\tfrac{3}{4}; x=12x=\tfrac{1}{2} cup
  4. Equation: x+14=34x+\tfrac{1}{4}=\tfrac{3}{4}; x=14x=\tfrac{1}{4} cup
Explanation: This question tests writing and solving one-step equations of the form x + p = q from real-world problems with nonnegative rational numbers, using inverse operations. One-step equations in addition form x + p = q are solved by subtracting p from both sides to get x = q - p; for example, if x + 15 = 42, then x = 42 - 15 = 27, and inverse operations undo the original by subtracting for addition, with nonnegative rationals like fractions such as x = 1/2 from x + 1/4 = 3/4, all values ≥0. For instance, if you have x cups and add 1/4 cup to reach 3/4 cup, the equation is x + 1/4 = 3/4, solved by x = 3/4 - 1/4 = 1/2, meaning 1/2 cup more is needed; similarly, for decimals, x + 0.35 = 1.2 gives x = 0.85 liters. In this problem, the amount still needed x plus 1/4 cup poured equals 3/4 cup total, so the correct equation is x + 1/4 = 3/4, and solving gives x = 3/4 - 1/4 = 1/2 cup. Common errors include wrong fraction subtraction like computing 3/4 - 1/4 as 1/4 or 1 instead of 1/2, or using subtraction equation x - 1/4 = 3/4 leading to x = 1. To solve, (1) write the equation from context where 'already poured' means addition to reach total, (2) identify the form x + p = q, (3) apply inverse by subtracting p, (4) calculate 3/4 - 1/4 = 1/2, (5) verify 1/2 + 1/4 = 3/4, and (6) interpret as 1/2 cup still needed. Remember, all values are nonnegative fractions, and mistakes often involve incorrect common denominators or not verifying.

Question 7

A student read some pages, then read 1818 more pages and finished the book at 6565 pages total. Let xx be the number of pages the student had read before reading the last 1818 pages. Write and solve a one-step equation.

  1. Equation: x+18=65x+18=65; solution: x=83x=83 pages
  2. Equation: 18x=6518x=65; solution: x=6518x=\tfrac{65}{18} pages
  3. Equation: x−18=65x-18=65; solution: x=47x=47 pages
  4. Equation: x+18=65x+18=65; solution: x=47x=47 pages (correct answer)
Explanation: This question tests writing and solving one-step equations of the form x + p = q or p x = q from real-world problems involving nonnegative rational numbers, using inverse operations to solve. One-step equations include the addition form x + p = q solved by subtracting p from both sides to get x = q - p, for example, if x + 15 = 42, then x = 42 - 15 = 27; or the multiplication form p x = q solved by dividing both sides by p to get x = q / p, for example, if 6x = 18, then x = 18 ÷ 6 = 3; inverse operations undo the original operation, so addition is undone by subtraction and multiplication by division, with nonnegative rational numbers like whole numbers (x=27, p=15, q=42), fractions (x=1/2 from x + 1/4 = 3/4), or decimals (x=4 from 2.5x = 10), all greater than or equal to zero. For example, Maria has x dollars, earns $15, and now has $42, so the equation is x + 15 = 42, solved by subtracting 15 to get x = 27, meaning she started with $27; or for 6 items at $x each totaling $18, the equation is 6x = 18, solved by dividing by 6 to get x = 3, so each costs $3; or with fractions, x + 1/4 = 3/4, solved as x = 3/4 - 1/4 = 1/2 cup. In this problem, the correct equation is x + 18 = 65, solved by subtracting 18 to get x = 47 pages, meaning 47 pages were read before the last 18. A common error is adding instead of subtracting like choice B (65 + 18 = 83), using subtraction in equation like choice C, or setting up multiplication like choice D. To solve these problems: (1) write the equation from the context, identifying the operation such as 'then read 18 more' meaning addition, (2) identify the form as x + p = q or p x = q, (3) apply the inverse operation like subtracting p or dividing by p, (4) calculate accurately, such as 65 - 18 = 47, (5) verify by substituting back, like 47 + 18 = 65, and (6) interpret the solution in context, such as x = 47 means 47 pages before. Remember, all values are nonnegative, including whole numbers, fractions, or decimals greater than or equal to zero, and avoid mistakes like wrong operation, arithmetic errors, or wrong setup.

Question 8

A science club is making slime. They need 6 equal scoops of glitter to make a total of 1.5 cups of glitter. Let xx be the amount of glitter in one scoop (in cups). Write and solve an equation, and choose the correct interpretation.

  1. Equation: 6x=1.56x=1.5; x=9x=9 cup per scoop
  2. Equation: 6x=1.56x=1.5; x=0.25x=0.25 cup per scoop (correct answer)
  3. Equation: x+6=1.5x+6=1.5; x= ⁣−4.5x=\!-4.5 cups per scoop
  4. Equation: 6x=1.56x=1.5; x=1.5−6=4.5x=1.5-6=4.5 cups per scoop
Explanation: This question tests writing and solving one-step equations of the form px = q from real-world problems with nonnegative rational numbers, using inverse operations. One-step equations in multiplication form px = q are solved by dividing both sides by p to get x = q / p; for example, if 6x = 18, then x = 18 ÷ 6 = 3, and inverse operations undo the original by dividing for multiplication, with nonnegative rationals like decimals such as x = 0.25 from 6x = 1.5, all values ≥0. For instance, if 6 scoops are x cups each for 1.5 cups total, the equation is 6x = 1.5, solved by x = 1.5 ÷ 6 = 0.25, meaning 0.25 cup per scoop; similarly, for whole numbers, 8x = 4 gives x = 0.5. In this problem, 6 scoops at x each make 1.5 cups total, so the correct equation is 6x = 1.5, and solving gives x = 1.5 ÷ 6 = 0.25 cup per scoop. Common errors include subtraction like x = 1.5 - 6 = -4.5 (negative, not allowed), or arithmetic like x = 1.5 ÷ 6 = 9 or x = 4.5. To solve, (1) write the equation from context where 'equal scoops' means multiplication, (2) identify the form px = q, (3) apply inverse by dividing by p, (4) calculate 1.5 ÷ 6 = 0.25, (5) verify 6 × 0.25 = 1.5, and (6) interpret as 0.25 cup per scoop. Remember, all values are nonnegative, avoiding negatives, and mistakes often involve wrong operations or division errors.

Question 9

Solve the equation 2.5x=102.5x=10. What is xx?

  1. x=40x=40
  2. x=4x=4 (correct answer)
  3. x=2x=2
  4. x=25x=25
Explanation: This question tests solving one-step equations of the form px = q with nonnegative rational numbers, using inverse operations. One-step equations in multiplication form px = q are solved by dividing both sides by p to get x = q / p; for example, if 6x = 18, then x = 18 ÷ 6 = 3, and inverse operations undo the original by dividing for multiplication, with nonnegative rationals like decimals such as x = 4 from 2.5x = 10, all values ≥0. For instance, 2.5x = 10 is solved by x = 10 ÷ 2.5 = 4; similarly, for fractions, 2x = 1/2 gives x = 1/4. In this problem, the correct solution for 2.5x = 10 is x = 10 ÷ 2.5 = 4. Common errors include multiplying like x = 2.5 × 10 = 25, or wrong division like x = 2.5 ÷ 10 = 0.25 or x = 40. To solve, (1) identify the form px = q, (2) apply inverse by dividing by p, (3) calculate 10 ÷ 2.5 = 4, (4) verify 2.5 × 4 = 10. Remember, all values are nonnegative, and mistakes often involve arithmetic errors in decimal division or confusing operations.

Question 10

The cost of renting a kayak is $12 per hour. If Chen paid $42 total and there was no additional fee, how many hours did he rent the kayak?

  1. 2.52.5 hours
  2. 3.53.5 hours (correct answer)
  3. 4.54.5 hours
  4. 5.55.5 hours
Explanation: Setting up the equation: 12h = 42, where h is hours. Dividing both sides by 12: h = 42 ÷ 12 = 3.5 hours. Choice A (2.5) would cost $30. Choice C (4.5) would cost $54. Choice D (5.5) would cost $66.

Question 11

A science lab has 34\tfrac{3}{4} cup of saltwater mixture after adding 14\tfrac{1}{4} cup of water. Let xx be the amount of mixture before adding water. Write an equation of the form x+p=qx+p=q and solve for xx.

  1. x=1x=1 cup
  2. x=14x=\tfrac{1}{4} cup
  3. x=12x=\tfrac{1}{2} cup (correct answer)
  4. x=34x=\tfrac{3}{4} cup
Explanation: This question tests writing and solving one-step equations of the form x + p = q from real-world problems with nonnegative rational numbers, using inverse operations. One-step equations in addition form x + p = q are solved by subtracting p from both sides to get x = q - p; for example, if x + 15 = 42, then x = 42 - 15 = 27, and for multiplication form p x = q, solve by dividing both sides by p to get x = q / p, like 6x = 18 gives x = 18 ÷ 6 = 3. Inverse operations undo the original operation: addition is undone by subtraction, and multiplication by division, with nonnegative rational numbers including whole numbers like x=27, p=15, q=42, fractions such as x=1/2 from x + 1/4 = 3/4, or decimals like x=4 from 2.5x=10, all greater than or equal to zero. For example, if Maria has x dollars, earns $15, and now has $42, the equation is x + 15 = 42, solved by subtracting 15 to get x = 27, meaning she started with $27; or for 6 items at $x each totaling $18, it's 6x = 18, divided by 6 to get x = 3, so each costs $3; or with fractions, x + 1/4 = 3/4 gives x = 3/4 - 1/4 = 1/2 cup. In this case, the correct equation is x + 1/4 = 3/4, solved as x = 3/4 - 1/4 = 2/4 = 1/2 cup, so the initial amount was 1/2 cup. Common errors include fraction operation mistakes like subtracting numerators without common denominators to get 3/4 - 1/4 = 2/0 or something wrong like 3-1=2 over 4-4=0, or setting up as x - 1/4 = 3/4 leading to x=1. To solve, (1) write the equation from the context where 'adding 1/4 cup' means add 1/4, (2) identify the addition form, (3) apply subtraction as the inverse, (4) calculate 3/4 - 1/4 = 1/2, (5) verify by substituting 1/2 + 1/4 = 3/4, and (6) interpret as initial 1/2 cup; remember all values are nonnegative, and avoid mistakes like wrong fraction operations or not verifying.

Question 12

A water bottle had some water in it. Then 0.750.75 liters were poured in, and now the bottle has 2.002.00 liters. Let xx be the amount of water originally in the bottle. Write and solve a one-step equation.

  1. Equation: x−0.75=2.00x-0.75=2.00; solution: x=1.25x=1.25 liters
  2. Equation: x+0.75=2.00x+0.75=2.00; solution: x=1.25x=1.25 liters (correct answer)
  3. Equation: x+0.75=2.00x+0.75=2.00; solution: x=2.75x=2.75 liters
  4. Equation: 0.75x=2.000.75x=2.00; solution: x=2.75x=2.75 liters
Explanation: This question tests writing and solving one-step equations of the form x + p = q or p x = q from real-world problems involving nonnegative rational numbers, using inverse operations to solve. One-step equations include the addition form x + p = q solved by subtracting p from both sides to get x = q - p, for example, if x + 15 = 42, then x = 42 - 15 = 27; or the multiplication form p x = q solved by dividing both sides by p to get x = q / p, for example, if 6x = 18, then x = 18 ÷ 6 = 3; inverse operations undo the original operation, so addition is undone by subtraction and multiplication by division, with nonnegative rational numbers like whole numbers (x=27, p=15, q=42), fractions (x=1/2 from x + 1/4 = 3/4), or decimals (x=4 from 2.5x = 10), all greater than or equal to zero. For example, Maria has x dollars, earns $15, and now has $42, so the equation is x + 15 = 42, solved by subtracting 15 to get x = 27, meaning she started with $27; or for 6 items at $x each totaling $18, the equation is 6x = 18, solved by dividing by 6 to get x = 3, so each costs $3; or with fractions, x + 1/4 = 3/4, solved as x = 3/4 - 1/4 = 1/2 cup. In this problem, the correct equation is x + 0.75 = 2.00, solved by subtracting 0.75 to get x = 1.25 liters, meaning originally 1.25 liters. A common error is adding instead of subtracting like choice B (2.00 + 0.75 = 2.75), setting up multiplication like choice C, or using subtraction in equation but correct calculation in choice D (wrong form). To solve these problems: (1) write the equation from the context, identifying the operation such as 'poured in' meaning addition, (2) identify the form as x + p = q or p x = q, (3) apply the inverse operation like subtracting p or dividing by p, (4) calculate accurately, such as 2.00 - 0.75 = 1.25, (5) verify by substituting back, like 1.25 + 0.75 = 2.00, and (6) interpret the solution in context, such as x = 1.25 means 1.25 liters originally. Remember, all values are nonnegative, including whole numbers, fractions, or decimals greater than or equal to zero, and avoid mistakes like wrong operation, decimal subtraction errors, or setup issues.

Question 13

The temperature dropped by the same amount each hour for 6 hours. If the total temperature drop was 18°F18°F, by how much did the temperature drop each hour?

  1. 2°F2°F
  2. 3°F3°F (correct answer)
  3. 4°F4°F
  4. 6°F6°F
Explanation: Setting up the equation: 6d = 18, where d is the drop per hour. Solving: d = 18 ÷ 6 = 3°F per hour. Choice A would give a total drop of 6 × 2 = 12°F. Choice C would give a total drop of 6 × 4 = 24°F. Choice D would give a total drop of 6 × 6 = 36°F.

Question 14

A pack of stickers has 6 identical sheets. The total cost is $18. Write and solve an equation of the form $px=qtofindthecostto find the costx$ of one sheet.

  1. x=18x=18 dollars per sheet
  2. x=108x=108 dollars per sheet
  3. x=12x=12 dollars per sheet
  4. x=3x=3 dollars per sheet (correct answer)
Explanation: This question tests writing and solving one-step equations of the form p x = q from real-world problems with nonnegative rational numbers, using inverse operations. One-step equations in addition form x + p = q are solved by subtracting p from both sides to get x = q - p; for example, if x + 15 = 42, then x = 42 - 15 = 27, and for multiplication form p x = q, solve by dividing both sides by p to get x = q / p, like 6x = 18 gives x = 18 ÷ 6 = 3. Inverse operations undo the original operation: addition is undone by subtraction, and multiplication by division, with nonnegative rational numbers including whole numbers like x=27, p=15, q=42, fractions such as x=1/2 from x + 1/4 = 3/4, or decimals like x=4 from 2.5x=10, all greater than or equal to zero. For example, if Maria has x dollars, earns $15, and now has $42, the equation is x + 15 = 42, solved by subtracting 15 to get x = 27, meaning she started with $27; or for 6 items at $x each totaling $18, it's 6x = 18, divided by 6 to get x = 3, so each costs $3; or with fractions, x + 1/4 = 3/4 gives x = 3/4 - 1/4 = 1/2 cup. In this case, the correct equation is 6x = 18, solved as x = 18 ÷ 6 = 3, so each sheet costs $3. Common errors include using the wrong operation like subtracting instead of dividing to get something like x = 18 - 6 = 12, or arithmetic mistakes in division like 18 ÷ 6 = 2 or 108 somehow, or setting up the equation as x + 6 = 18. To solve, (1) write the equation from the context where '6 sheets at x each' means multiply by 6, (2) identify the multiplication form, (3) apply division as the inverse, (4) calculate 18 ÷ 6 = 3, (5) verify by substituting 6 × 3 = 18, and (6) interpret as $3 per sheet; remember all values are nonnegative, and avoid mistakes like wrong operations or not verifying the solution.

Question 15

A water bottle holds 1.2 liters when full. After adding 0.35 liters, it became full. Let xx be the amount of water already in the bottle before adding. Write an equation and solve for xx.

  1. Equation: x−0.35=1.2x-0.35=1.2; x=0.85x=0.85 liters
  2. Equation: x+0.35=1.2x+0.35=1.2; x=0.85x=0.85 liters (correct answer)
  3. Equation: x+0.35=1.2x+0.35=1.2; x=1.55x=1.55 liters
  4. Equation: x+0.35=1.2x+0.35=1.2; x=0.35x=0.35 liters
Explanation: This question tests writing and solving one-step equations of the form x + p = q from real-world problems with nonnegative rational numbers, using inverse operations. One-step equations in addition form x + p = q are solved by subtracting p from both sides to get x = q - p; for example, if x + 15 = 42, then x = 42 - 15 = 27, and inverse operations undo the original by subtracting for addition, with nonnegative rationals like decimals such as x = 0.85 from x + 0.35 = 1.2, all values ≥0. For instance, if a bottle has x liters and adding 0.35 liters reaches 1.2 liters, the equation is x + 0.35 = 1.2, solved by x = 1.2 - 0.35 = 0.85, meaning 0.85 liters were already there; similarly, for fractions, x + 1/4 = 3/4 gives x = 1/2. In this problem, the amount already in x plus 0.35 added equals 1.2 full, so the correct equation is x + 0.35 = 1.2, and solving gives x = 1.2 - 0.35 = 0.85 liters. Common errors include adding instead of subtracting like x = 1.2 + 0.35 = 1.55, or using subtraction equation x - 0.35 = 1.2 leading to x = 1.55. To solve, (1) write the equation from context where 'after adding' means addition to reach full, (2) identify the form x + p = q, (3) apply inverse by subtracting p, (4) calculate 1.2 - 0.35 = 0.85, (5) verify 0.85 + 0.35 = 1.2, and (6) interpret as 0.85 liters already. Remember, all values are nonnegative decimals, and mistakes often involve wrong arithmetic or setup.

Question 16

Solve the equation x+0.35=1.20x+0.35=1.20. What is xx?

  1. x=1.55x=1.55
  2. x=0.85x=0.85 (correct answer)
  3. x=0.35x=0.35
  4. x=1.20x=1.20
Explanation: This question tests solving one-step equations of the form x + p = q with nonnegative rational numbers, using inverse operations. One-step equations in addition form x + p = q are solved by subtracting p from both sides to get x = q - p; for example, if x + 15 = 42, then x = 42 - 15 = 27, and for multiplication form p x = q, solve by dividing both sides by p to get x = q / p, like 6x = 18 gives x = 18 ÷ 6 = 3. Inverse operations undo the original operation: addition is undone by subtraction, and multiplication by division, with nonnegative rational numbers including whole numbers like x=27, p=15, q=42, fractions such as x=1/2 from x + 1/4 = 3/4, or decimals like x=4 from 2.5x=10, all greater than or equal to zero. For example, if Maria has x dollars, earns $15, and now has $42, the equation is x + 15 = 42, solved by subtracting 15 to get x = 27, meaning she started with $27; or for 6 items at $x each totaling $18, it's 6x = 18, divided by 6 to get x = 3, so each costs $3; or with fractions, x + 1/4 = 3/4 gives x = 3/4 - 1/4 = 1/2 cup. In this case, the equation is x + 0.35 = 1.20, solved as x = 1.20 - 0.35 = 0.85. Common errors include adding instead of subtracting to get x = 1.20 + 0.35 = 1.55, or decimal subtraction mistakes like 1.20 - 0.35 = 1.55 or 0.35. To solve, (1) identify the addition form from the equation, (2) apply subtraction as the inverse, (3) calculate 1.20 - 0.35 = 0.85, (4) verify by substituting 0.85 + 0.35 = 1.20; remember all values are nonnegative, and avoid mistakes like wrong operations or arithmetic errors.

Question 17

A movie rental costs the same amount each time. Maya rented 5 movies and paid $17.50 total. Let xx be the cost of one rental. Write and solve an equation of the form px=qpx=q.

  1. Equation: 5x=17.505x=17.50; x=17.50−5=12.50x=17.50-5=12.50 dollars
  2. Equation: x+5=17.50x+5=17.50; x=12.50x=12.50 dollars
  3. Equation: 5x=17.505x=17.50; x=3.50x=3.50 dollars (correct answer)
  4. Equation: 5x=17.505x=17.50; x=22.50x=22.50 dollars
Explanation: This question tests writing and solving one-step equations of the form px=qpx = q from real-world problems with nonnegative rational numbers, using inverse operations. One-step equations in multiplication form px=qpx = q are solved by dividing both sides by pp to get x=q/px = q / p; for example, if 6x=186x = 18, then x=18÷6=3x = 18 \div 6 = 3, and inverse operations undo the original by dividing for multiplication, with nonnegative rationals like decimals such as x=3.50x = 3.50 from 5x=17.505x = 17.50, all values ≥0\geq0. For instance, if 5 rentals cost xx each for $17.50 total, the equation is 5x=17.505x = 17.50, solved by x=17.50÷5=3.50x = 17.50 \div 5 = 3.50, meaning each costs $3.50; similarly, for whole numbers, 8x=48x = 4 gives x=0.5x = 0.5. In this problem, 5 movies at xx each cost $17.50 total, so the correct equation is 5x=17.505x = 17.50, and solving gives x=17.50÷5=3.50x = 17.50 \div 5 = 3.50 dollars. Common errors include using subtraction like x=17.50−5=12.50x = 17.50 - 5 = 12.50, or wrong operation like x+5=17.50x + 5 = 17.50 giving x=12.50x = 12.50, or division error like x=22.50x = 22.50. To solve, (1) write the equation from context where 'same amount each time' means multiplication, (2) identify the form px=qpx = q, (3) apply inverse by dividing by pp, (4) calculate 17.50÷5=3.5017.50 \div 5 = 3.50, (5) verify 5×3.50=17.505 \times 3.50 = 17.50, and (6) interpret as $3.50 per rental. Remember, all values are nonnegative, and mistakes often involve confusing addition with multiplication or arithmetic errors.

Question 18

Which value of xx makes the equation x+25=1x+\tfrac{2}{5}=1 true?

  1. x=55x=\tfrac{5}{5}
  2. x=35x=\tfrac{3}{5} (correct answer)
  3. x=25x=\tfrac{2}{5}
  4. x=75x=\tfrac{7}{5}
Explanation: This question tests solving one-step equations of the form x + p = q with nonnegative rational numbers, using inverse operations. One-step equations in addition form x + p = q are solved by subtracting p from both sides to get x = q - p; for example, if x + 15 = 42, then x = 42 - 15 = 27, and inverse operations undo the original by subtracting for addition, with nonnegative rationals like fractions such as x = 1/2 from x + 1/4 = 3/4, all values ≥0. For instance, x + 2/5 = 1 is solved by x = 1 - 2/5 = 3/5; similarly, for whole numbers, x + 9 = 26 gives x = 17. In this problem, the value that makes x + 2/5 = 1 true is x = 1 - 2/5 = 3/5. Common errors include adding like x = 1 + 2/5 = 7/5, or fraction mistakes like x = 2/5 or 5/5 = 1. To solve, (1) identify the form x + p = q, (2) apply inverse by subtracting p, (3) calculate 1 - 2/5 = 3/5 (using common denominator), (4) verify 3/5 + 2/5 = 5/5 = 1. Remember, all values are nonnegative fractions, and mistakes often involve incorrect subtraction or not using common denominators.

Question 19

Solve the equation 12x=6\tfrac{1}{2}x=6. What is xx?

  1. x=5.5x=5.5
  2. x=6.5x=6.5
  3. x=12x=12 (correct answer)
  4. x=3x=3
Explanation: This question tests solving one-step equations of the form p x = q with nonnegative rational numbers, using inverse operations. One-step equations in addition form x + p = q are solved by subtracting p from both sides to get x = q - p; for example, if x + 15 = 42, then x = 42 - 15 = 27, and for multiplication form p x = q, solve by dividing both sides by p to get x = q / p, like 6x = 18 gives x = 18 ÷ 6 = 3. Inverse operations undo the original operation: addition is undone by subtraction, and multiplication by division, with nonnegative rational numbers including whole numbers like x=27, p=15, q=42, fractions such as x=1/2 from x + 1/4 = 3/4, or decimals like x=4 from 2.5x=10, all greater than or equal to zero. For example, if Maria has x dollars, earns $15, and now has $42, the equation is x + 15 = 42, solved by subtracting 15 to get x = 27, meaning she started with $27; or for 6 items at $x each totaling $18, it's 6x = 18, divided by 6 to get x = 3, so each costs $3; or with fractions, x + 1/4 = 3/4 gives x = 3/4 - 1/4 = 1/2 cup. In this case, the equation is (1/2)x = 6, solved as x = 6 ÷ (1/2) = 12, or equivalently multiply by 2 to get x=12. Common errors include multiplying instead of dividing incorrectly like (1/2)x=6 giving x=3, or treating it as addition. To solve, (1) identify the multiplication form from the equation, (2) apply division by 1/2 as the inverse (or multiply by 2), (3) calculate 6 × 2 = 12, (4) verify by substituting (1/2) × 12 = 6; remember all values are nonnegative, and avoid mistakes like wrong inverse or arithmetic errors.

Question 20

A school fundraiser collected $58 after a donation of $12 was added. Let xx be the amount collected before the donation. Write a one-step equation and solve for xx.

  1. Equation: x−12=58x-12=58; solution: x=70x=70
  2. Equation: 12x=5812x=58; solution: x=296x=\tfrac{29}{6}
  3. Equation: x+12=58x+12=58; solution: x=46x=46 (correct answer)
  4. Equation: x+12=58x+12=58; solution: x=70x=70
Explanation: This question tests writing and solving one-step equations of the form x + p = q or p x = q from real-world problems involving nonnegative rational numbers, using inverse operations to solve. One-step equations include the addition form x + p = q solved by subtracting p from both sides to get x = q - p, for example, if x + 15 = 42, then x = 42 - 15 = 27; or the multiplication form p x = q solved by dividing both sides by p to get x = q / p, for example, if 6x = 18, then x = 18 ÷ 6 = 3; inverse operations undo the original operation, so addition is undone by subtraction and multiplication by division, with nonnegative rational numbers like whole numbers (x=27, p=15, q=42), fractions (x=1/2 from x + 1/4 = 3/4), or decimals (x=4 from 2.5x = 10), all greater than or equal to zero. For example, Maria has x dollars, earns $15, and now has $42, so the equation is x + 15 = 42, solved by subtracting 15 to get x = 27, meaning she started with $27; or for 6 items at $x each totaling $18, the equation is 6x = 18, solved by dividing by 6 to get x = 3, so each costs $3; or with fractions, x + 1/4 = 3/4, solved as x = 3/4 - 1/4 = 1/2 cup. In this problem, the correct equation is x + 12 = 58, solved by subtracting 12 to get x = 46, meaning $46 was collected before the donation. A common error is setting up the wrong equation like x - 12 = 58 (choice B) or 12x = 58 (choice C), or solving incorrectly like adding instead of subtracting in choice D (x = 58 + 12 = 70). To solve these problems: (1) write the equation from the context, identifying the operation such as 'added' meaning addition, (2) identify the form as x + p = q or p x = q, (3) apply the inverse operation like subtracting p or dividing by p, (4) calculate accurately, such as 58 - 12 = 46, (5) verify by substituting back, like 46 + 12 = 58, and (6) interpret the solution in context, such as x = 46 means $46 before the donation. Remember, all values are nonnegative, including whole numbers, fractions, or decimals greater than or equal to zero, and avoid mistakes like using the wrong operation, arithmetic errors, or failing to verify the solution.