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 + 1/4 = 3/4, solved by subtracting 1/4 to get x = 1/2 cup, meaning 1/2 cup is still needed. A common error is solving incorrectly like subtracting wrong in choice B (x = 3/4 - 1/4 = 1/2 but listed as 1), setting up multiplication instead like choice C, or using subtraction in the equation like choice D with wrong form but correct calculation. 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 3/4 - 1/4 = 1/2, (5) verify by substituting back, like 1/2 + 1/4 = 3/4, and (6) interpret the solution in context, such as x = 1/2 means 1/2 cup still needed. Remember, all values are nonnegative, including whole numbers, fractions, or decimals greater than or equal to zero, and avoid mistakes like fraction operation errors, wrong setup, or not verifying.

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.

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.

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.

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.

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.

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.

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.

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.

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.