SSAT Middle Level Quiz: One Step Equations
20 questions · exam conditions
0:00
One Step EquationsQuestion 1 of 20

At a bake sale, 4x=284x = 28; find xx.

6
7
24
8
← Back to quizzes

SSAT Middle Level Quiz

SSAT Middle Level Quiz: One Step Equations

Practice One Step Equations in SSAT Middle Level 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 One Step Equations, giving you a quick way to practice the rules, question types, and explanations that matter most for SSAT Middle Level.

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

At a bake sale, 4x=284x = 28; find xx.

  1. 6
  2. 7 (correct answer)
  3. 24
  4. 8
Explanation: This question tests middle-level algebra skills: solving one-step equations with a variable. Understanding one-step equations involves performing inverse operations to isolate the variable. For example, if 4x = 20, divide both sides by 4 to solve for x. In this specific question, the equation 4x = 28 requires dividing both sides by 4, resulting in x = 7. Choice B is correct because it accurately reflects the solution to the equation. Choice C is incorrect as it results from multiplying instead of dividing, a common mistake when students misinterpret the operation needed. To help students: Encourage practicing inverse operations, using division facts for visualization, and checking solutions by substituting back into the original equation. Watch for: misunderstanding inverse operations, and ensure clarity in distinguishing between multiplication and division.

Question 2

Maria bought a notebook and spent $3 more than twice what she had planned to spend. If she actually spent $15, how much had she planned to spend?

  1. $6 (correct answer)
  2. $9
  3. $12
  4. $18
  5. $21
Explanation: This is a classic "working backwards" word problem that tests your ability to translate English into algebra. When you see phrases like "more than twice," you need to carefully set up an equation based on what actually happened. Let's call the planned amount pp. The problem states Maria spent "$3 more than twice what she had planned," which translates to $2p+32p + 3 .Sincesheactuallyspent$15,wecanwrite:$. Since she actually spent $15, we can write: $2p + 3 = 15$$ Solving for pp: 2p+3=152p + 3 = 15 2p=122p = 12 p=6p = 6 So Maria had planned to spend $6, making (A) correct. Let's check why the other answers don't work. If you choose (B) $9, then twice that plus $3 would be $2(9) + 3 = 21$$, not $15. For (C) $12, you get $2(12) + 3 = 27 , which is way too high. Answer (D) $18 gives you $$2(18) + 3 = 39$$, which is even further off. The most common mistake here is confusing the relationship. Some students might think "she spent $3 more" means you add 3totheactualamountspent(3 to the actual amount spent (15 + $3 = $18), leading them to pick (D). Others might subtract $3 from $15 to get $12, choosing (C). Strategy tip: Always define your variable as what the question asks for (here, "planned to spend"), then translate the word problem into an equation step by step. Don't try to shortcut the algebra—write it out clearly to avoid mix-ups with the relationships.

Question 3

A rectangle has a width that is 5 inches less than its length. If the width is 12 inches, what is the length?

  1. 7 inches
  2. 17 inches (correct answer)
  3. 60 inches
  4. 24 inches
  5. 144 inches
Explanation: When you see a word problem about relationships between dimensions, you need to carefully translate the words into mathematical expressions and identify what you're solving for. The problem states that the width is 5 inches less than the length, and the width is 12 inches. Let's call the length ll. The relationship "width is 5 inches less than length" translates to: width=l−5\text{width} = l - 5 Since we know the width is 12 inches, we can substitute: 12=l−512 = l - 5 To solve for the length, add 5 to both sides: 12+5=l12 + 5 = l, so l=17l = 17 inches. Let's check each answer choice. Choice A (7 inches) comes from the common error of subtracting instead of adding: 12−5=712 - 5 = 7. This misinterprets the relationship direction. Choice C (60 inches) likely results from multiplying 12 × 5, which doesn't match the "less than" relationship described. Choice D (24 inches) comes from incorrectly adding 12 + 12, perhaps confusing this with a perimeter calculation. Choice B (17 inches) is correct because when the length is 17 inches, the width would indeed be 17−5=1217 - 5 = 12 inches, matching the given information. Strategy tip: In word problems involving relationships between quantities, always define your variable for the unknown, write the relationship as an equation, then substitute known values. Double-check by plugging your answer back into the original relationship to verify it makes sense.

Question 4

Tom's age in 6 years will be 21. How old is Tom now?

  1. 15 years old (correct answer)
  2. 16 years old
  3. 21 years old
  4. 27 years old
  5. 126 years old
Explanation: Age problems involve working backward from future information to find present values. When you see a question telling you someone's age at a future time, you need to subtract the number of years to find their current age. Let's set up the problem systematically. If Tom's age in 6 years will be 21, we can write this as: Tom's current age + 6 = 21. To find Tom's current age, we subtract 6 from both sides: Tom's current age = 21 - 6 = 15 years old. We can verify this: if Tom is currently 15, then in 6 years he'll be 15 + 6 = 21 years old, which matches the given information. Looking at the wrong answers: Choice B (16 years old) is close but represents adding one extra year — if Tom were 16 now, he'd be 22 in 6 years, not 21. Choice C (21 years old) is the trap of using his future age as his current age; if he's 21 now, he'd be 27 in 6 years. Choice D (27 years old) comes from mistakenly adding 6 to 21 instead of subtracting; this would make Tom 33 years old in 6 years. For age problems, always identify what time period you're given information about, then work backward or forward as needed. When the problem states "age in X years will be Y," use the formula: current age = Y - X. Double-check by adding the years back to your answer.

Question 5

Sarah has some stickers. After giving away 15 stickers, she has 42 stickers left. How many stickers did Sarah start with?

  1. 27 stickers
  2. 57 stickers (correct answer)
  3. 630 stickers
  4. 84 stickers
  5. 2.8 stickers
Explanation: This is a classic "working backwards" word problem that tests your ability to set up and solve a simple equation. When you see phrases like "after giving away" or "has left," you need to think about the relationship between the starting amount, what changed, and the final result. Let's work through this step by step. Sarah started with some unknown number of stickers, gave away 15, and ended up with 42. If we call her starting amount xx, then: x−15=42x - 15 = 42. To find xx, we add 15 to both sides: x=42+15=57x = 42 + 15 = 57 stickers. You can verify this makes sense: if Sarah started with 57 stickers and gave away 15, she would have 57−15=4257 - 15 = 42 stickers remaining, which matches the problem. Looking at the wrong answers: Choice A (27) represents the common error of subtracting instead of adding—students might think 42−15=2742 - 15 = 27, but this doesn't answer what we're looking for. Choice C (630) is the result of multiplying 42×1542 \times 15, which doesn't make logical sense in this context. Choice D (84) comes from adding 42+4242 + 42, perhaps from misreading the problem or confusing the numbers involved. Strategy tip: For "working backwards" problems, always check your answer by plugging it back into the original situation. This verification step catches most calculation errors and helps confirm you set up the problem correctly. The key phrase "after giving away... left" should immediately signal addition to reverse the subtraction that occurred.

Question 6

If −2m=18-2m = 18, what is the value of mm?

  1. −36-36
  2. −9-9 (correct answer)
  3. 9
  4. 16
  5. 20
Explanation: This question tests your ability to solve a basic linear equation with negative coefficients. When you see an equation like this, you need to isolate the variable by performing the same operation on both sides. Starting with −2m=18-2m = 18, you want to get mm by itself. Since mm is being multiplied by −2-2, you need to divide both sides by −2-2: −2m−2=18−2\frac{-2m}{-2} = \frac{18}{-2} On the left side, −2m−2=m\frac{-2m}{-2} = m. On the right side, 18−2=−9\frac{18}{-2} = -9. Therefore, m=−9m = -9. You can verify this: if m=−9m = -9, then −2(−9)=18-2(-9) = 18, which checks out. Looking at the wrong answers: Choice A (−36-36) comes from multiplying both sides by −2-2 instead of dividing, giving you (−2)(−2m)=(−2)(18)(-2)(-2m) = (-2)(18), or 4m=−364m = -36. Choice C (99) results from forgetting that dividing by a negative number makes the answer negative—you'd get this if you incorrectly calculated 18−2=9\frac{18}{-2} = 9. Choice D (1616) doesn't follow from any logical algebraic step and might come from misreading the problem or making calculation errors. Remember this key principle: when solving equations, whatever operation you perform on one side must be performed on the other side. Also, pay careful attention to negative signs—dividing or multiplying by negative numbers changes the sign of your result.

Question 7

If 4(p+3)=284(p + 3) = 28, what is the value of pp?

  1. 4 (correct answer)
  2. 7
  3. 10
  4. 16
  5. 25
Explanation: This is a linear equation that you solve by isolating the variable pp using inverse operations. When you see an equation like this, work systematically to "undo" each operation in reverse order. Starting with 4(p+3)=284(p + 3) = 28, first divide both sides by 4 to eliminate the coefficient: p+3=7p + 3 = 7. Then subtract 3 from both sides to isolate pp: p=4p = 4. You can verify this by substituting back: 4(4+3)=4(7)=284(4 + 3) = 4(7) = 28 ✓ Looking at the wrong answers: Choice B (7) is what you get if you stop after the first step and forget to subtract 3 from p+3=7p + 3 = 7. This is a common error when students see that 7 appears in their work and mistakenly think it's the final answer. Choice C (10) results from adding 3 instead of subtracting it in the final step, giving p=7+3=10p = 7 + 3 = 10. Choice D (16) comes from incorrectly distributing or making an arithmetic error, possibly thinking 28−4×3=1628 - 4 \times 3 = 16. Remember to work through multi-step equations methodically: eliminate multiplication/division first, then handle addition/subtraction. Always check your answer by substituting it back into the original equation. This verification step catches most algebraic mistakes and builds confidence in your solution.

Question 8

Three times a number decreased by 5 equals 19. What is the number?

  1. 6
  2. 8 (correct answer)
  3. 14
  4. 24
  5. 57
Explanation: When you see "three times a number decreased by 5 equals 19," you're dealing with translating words into algebra. This type of word problem tests your ability to set up and solve equations systematically. Let's call the unknown number xx. Breaking down the phrase: "three times a number" means 3x3x, "decreased by 5" means subtract 5, so we get 3x−53x - 5. Since this "equals 19," our equation is 3x−5=193x - 5 = 19. To solve, add 5 to both sides: 3x−5+5=19+53x - 5 + 5 = 19 + 5, which gives us 3x=243x = 24. Dividing both sides by 3: x=8x = 8. Let's verify: three times 8 is 24, decreased by 5 gives us 19. ✓ Looking at the wrong answers: Choice A (6) comes from incorrectly setting up the equation as 3x+5=193x + 5 = 19 instead of 3x−5=193x - 5 = 19. This gives 3x=143x = 14, so x=4.67x = 4.67, but if you round or make calculation errors, you might pick 6. Choice C (14) results from forgetting to divide by 3 after finding 3x=243x = 24. Choice D (24) happens when you solve for 3x3x but forget that the question asks for xx, not 3x3x. The key strategy here is to translate the words methodically into mathematical symbols, then solve step by step. Always check your answer by substituting it back into the original word problem to ensure it makes sense.

Question 9

If −3x+7=−8-3x + 7 = -8, what is the value of xx?

  1. −5-5
  2. 13\frac{1}{3}
  3. 5 (correct answer)
  4. 15
  5. −15-15
Explanation: This is a linear equation that requires you to isolate the variable xx using inverse operations. When you see an equation like −3x+7=−8-3x + 7 = -8, your goal is to get xx by itself on one side. Start by subtracting 7 from both sides to eliminate the constant term: −3x+7−7=−8−7-3x + 7 - 7 = -8 - 7, which simplifies to −3x=−15-3x = -15. Next, divide both sides by −3-3 to isolate xx: −3x−3=−15−3\frac{-3x}{-3} = \frac{-15}{-3}. This gives you x=5x = 5. You can verify this by substituting back: −3(5)+7=−15+7=−8-3(5) + 7 = -15 + 7 = -8 ✓ Looking at the wrong answers: Choice (A) gives −5-5, which occurs if you forget that dividing two negative numbers yields a positive result—a common sign error. Choice (B) gives 13\frac{1}{3}, which suggests confusion about the order of operations or possibly dividing −3-3 by −15-15 instead of −15-15 by −3-3. Choice (D) gives 1515, which happens if you correctly get −3x=−15-3x = -15 but then incorrectly think x=15x = 15 by dropping the negative signs entirely. The correct answer is (C) 55. Study tip: Always work systematically with linear equations—handle addition/subtraction first, then multiplication/division. Pay special attention to negative signs, and always substitute your answer back into the original equation to check your work. This catches most algebraic mistakes before you submit your answer.

Question 10

If 2y+5y=212y + 5y = 21, what is the value of yy?

  1. 3 (correct answer)
  2. 7
  3. 16
  4. 21
  5. 147
Explanation: This is a linear equation with like terms that need to be combined before solving for the variable. When you see an equation like 2y+5y=212y + 5y = 21, start by combining the like terms on the left side. Since both terms contain the variable yy, you can add their coefficients: 2y+5y=(2+5)y=7y2y + 5y = (2 + 5)y = 7y. This simplifies your equation to 7y=217y = 21. To solve for yy, divide both sides by 7: y=217=3y = \frac{21}{7} = 3. Let's check why each answer choice is right or wrong: A) 3 is correct. Substituting back: 2(3)+5(3)=6+15=212(3) + 5(3) = 6 + 15 = 21 ✓ B) 7 represents a common error where students confuse the coefficient with the variable's value. After combining like terms to get 7y=217y = 21, some students mistakenly think y=7y = 7 instead of dividing properly. C) 16 might result from incorrectly subtracting instead of adding when combining like terms (5−2=35 - 2 = 3, then somehow getting to 16), or from other arithmetic errors in the solving process. D) 21 is the result of thinking that yy equals the number on the right side of the equation without doing any algebraic manipulation. Remember to always combine like terms first, then isolate the variable. After solving, substitute your answer back into the original equation to verify it works—this catches most computational errors and builds confidence in your solution.

Question 11

A recipe calls for 4 cups of flour to make 12 muffins. If Lisa wants to make 18 muffins, how many cups of flour does she need?

  1. 6 cups (correct answer)
  2. 8 cups
  3. 14 cups
  4. 22 cups
  5. 72 cups
Explanation: This is a proportion problem where you need to find how much of one ingredient you need when scaling a recipe up or down. When you see questions about recipes, rates, or "per unit" relationships, think about setting up proportions to maintain the same ratio. The original recipe uses 4 cups of flour for 12 muffins. To find how much flour Lisa needs for 18 muffins, set up a proportion: 4 cups12 muffins=x cups18 muffins\frac{4 \text{ cups}}{12 \text{ muffins}} = \frac{x \text{ cups}}{18 \text{ muffins}} Cross multiply: 4×18=12×x4 \times 18 = 12 \times x, which gives you 72=12x72 = 12x. Dividing both sides by 12: x=6x = 6 cups. You can also think of this as finding the rate first: 4 cups ÷ 12 muffins = 13\frac{1}{3} cup per muffin. Then multiply: 13×18=6\frac{1}{3} \times 18 = 6 cups. Looking at the wrong answers: B) 8 cups comes from incorrectly adding 4 cups to the original amount without considering the actual ratio needed. C) 14 cups might result from adding 18 - 12 = 6 to the original 4 cups plus some calculation error. D) 22 cups is far too large and suggests multiplying instead of using proportional reasoning. Study tip: For proportion problems on the SSAT, always check if your answer makes sense. Since Lisa is making 1.5 times as many muffins (18 ÷ 12 = 1.5), she should need 1.5 times as much flour: 4 × 1.5 = 6 cups. This "scaling factor" approach often provides a quick way to verify your answer.

Question 12

Carlos bought a shirt that was marked down from its original price. The sale price was $24, which was $8 less than the original price. What was the original price?

  1. $16
  2. $32 (correct answer)
  3. $192
  4. $3
  5. $200
Explanation: When you encounter word problems involving price changes, your goal is to translate the relationships described in words into mathematical equations. Here, you know the sale price is $24, and this amount is $8 less than the original price. Let's call the original price $x.Thephrase"$8lessthantheoriginalprice"meansyousubtract$8fromtheoriginalpricetogetthesaleprice:$. The phrase "$8 less than the original price" means you subtract $8 from the original price to get the sale price: $x - 8 = 24$$ To find the original price, add $8 to both sides: x=24+8=32x = 24 + 8 = 32 So the original price was $32. Let's check why the other answers are wrong. Choice (A) $16 represents a common error where students subtract instead of add: 24−8=1624 - 8 = 16. This gives you a number that's $8 less than the sale price, not the original price that's $8 more. Choice (C) $192 likely comes from multiplying 24×8=19224 × 8 = 192, which doesn't match the relationship described in the problem. Choice (D) $3 might result from dividing 24÷8=324 ÷ 8 = 3, again not addressing the actual relationship. You can verify choice (B) is correct: if the original price was $32 and it was marked down by $8, the sale price would be 32−8=2432 - 8 = 24 ✓ Strategy tip: In "less than" or "more than" problems, carefully identify what number is being compared to what. Draw a simple equation showing the relationship before solving, and always check your answer by plugging it back into the original situation.

Question 13

If k+62=9\frac{k + 6}{2} = 9, what is the value of kk?

  1. 3
  2. 12 (correct answer)
  3. 15
  4. 18
  5. 24
Explanation: This problem tests your ability to solve one-step equations involving fractions. When you see an equation with a variable in a fraction, your goal is to isolate the variable by undoing the operations in reverse order. Starting with k+62=9\frac{k + 6}{2} = 9, you need to eliminate the fraction first. Since (k+6)(k + 6) is divided by 2, multiply both sides by 2 to cancel out the denominator: k+6=18k + 6 = 18. Now subtract 6 from both sides to isolate kk: k=12k = 12. Let's verify: 12+62=182=9\frac{12 + 6}{2} = \frac{18}{2} = 9 ✓ Looking at the wrong answers: Choice (A) 3 likely comes from incorrectly solving k+6=9k + 6 = 9 without first multiplying by 2 to clear the fraction. Choice (C) 15 might result from adding 6 instead of subtracting it in the final step, giving k=18−6+3=15k = 18 - 6 + 3 = 15 through confused arithmetic. Choice (D) 18 comes from stopping too early—this is the value of k+6k + 6, not kk itself. The key strategy for fraction equations is to clear denominators first by multiplying both sides by the denominator, then solve the resulting simpler equation. Always check your answer by substituting back into the original equation. This verification step catches most algebraic mistakes and builds confidence in your solution.

Question 14

The sum of a number and 25 is 43. What is the number?

  1. 18 (correct answer)
  2. 68
  3. 1075
  4. 4325\frac{43}{25}
  5. −18-18
Explanation: This is a classic "translate words into algebra" problem that tests your ability to set up and solve a simple equation. When you see "the sum of a number and [something] is [total]," you're looking at an addition equation where one addend is unknown. Let's call the unknown number xx. The phrase "the sum of a number and 25" translates to x+25x + 25, and "is 43" means this equals 43. So our equation is: x+25=43x + 25 = 43 To solve for xx, subtract 25 from both sides: x=43−25=18x = 43 - 25 = 18 You can verify: 18+25=4318 + 25 = 43 ✓ Now let's examine why the other choices are wrong. Choice B (68) comes from adding instead of subtracting: 25+43=6825 + 43 = 68. This is a common error when students mix up the operations needed to solve versus the operations described in the problem. Choice C (1075) results from multiplying 25×4325 \times 43, which completely misinterprets "sum" as "product." Choice D (4325\frac{43}{25}) comes from dividing 43 by 25, another operation mix-up. The correct answer is A (18). Strategy tip: When solving word problems involving "sum," "difference," "product," or "quotient," always translate the words into an equation first, then solve using inverse operations. To find an unknown addend, subtract the known addend from the sum. Double-check by substituting your answer back into the original problem statement.

Question 15

The perimeter of a square is 48 inches. If each side length is represented by ss, which equation can be used to find ss?

  1. s+48=4s + 48 = 4
  2. 4s=484s = 48 (correct answer)
  3. s2=48s^2 = 48
  4. s=48÷2s = 48 ÷ 2
  5. 48s=448s = 4
Explanation: When you encounter a perimeter problem, remember that perimeter means the distance around the outside of a shape. For a square, since all four sides are equal, the perimeter equals 4 times the side length. Let's work through this systematically. If the square has side length ss, then the perimeter is s+s+s+s=4ss + s + s + s = 4s. Since we're told the perimeter is 48 inches, we can write the equation 4s=484s = 48. This directly translates the relationship between the four equal sides and the total perimeter. Looking at the wrong answers: Choice A (s+48=4s + 48 = 4) incorrectly adds the side length to the perimeter, which doesn't make mathematical sense and would give a negative side length. Choice C (s2=48s^2 = 48) confuses perimeter with area - you'd use s2s^2 if you were finding the area of the square, not the perimeter. Choice D (s=48÷2s = 48 ÷ 2) uses division by 2 instead of 4, which might come from thinking about a rectangle where you divide by 2 to account for length and width, but a square has four equal sides. You can verify: if 4s=484s = 48, then s=12s = 12. A square with 12-inch sides has perimeter 4×12=484 \times 12 = 48 inches. ✓ Study tip: For any polygon perimeter problem, write out what "perimeter" means for that specific shape. For squares and rectangles, remember the formulas: square perimeter = 4s4s, rectangle perimeter = 2l+2w2l + 2w.

Question 16

A number divided by 7 equals 8. What is the number?

  1. 1
  2. 15
  3. 56 (correct answer)
  4. 64
  5. 504
Explanation: When you see "a number divided by something equals something else," you're dealing with a division equation that you can solve by working backwards with multiplication. Let's call the unknown number xx. The problem states that x÷7=8x \div 7 = 8, or written as a fraction: x7=8\frac{x}{7} = 8. To find xx, multiply both sides by 7: x=8×7=56x = 8 \times 7 = 56. You can verify this: 56÷7=856 \div 7 = 8 ✓ Now let's see why the other answers don't work: Choice A) 1 would give us 1÷7=171 \div 7 = \frac{1}{7}, which is much less than 1, not 8. Choice B) 15 would give us 15÷7=21715 \div 7 = 2\frac{1}{7} (about 2.14), which is nowhere near 8. Choice D) 64 might be tempting because it's close to our answer, but 64÷7=91764 \div 7 = 9\frac{1}{7} (about 9.14), which overshoots our target of 8. The key strategy here is recognizing that division and multiplication are inverse operations. When you have "something divided by 7 equals 8," you can immediately think "8 times 7" to find that something. This backward-thinking approach—using the inverse operation—is your fastest path to the solution on these types of SSAT problems.

Question 17

A group raises 9696 selling xx tickets at 88 each: 8x=968x = 96.

  1. 104
  2. 12 (correct answer)
  3. 88
  4. 16
Explanation: This question tests middle-level algebra skills: solving one-step equations with a variable. Understanding one-step equations involves performing inverse operations to isolate the variable. For example, if 8x = 16, divide both sides by 8 to solve for x. In this specific question, the equation 8x = 96 requires dividing both sides by 8, resulting in x = 12. Choice B is correct because it accurately reflects the solution to the equation. Choice A is incorrect as it results from multiplying instead of dividing, a common mistake in fundraising. To help students: Encourage practicing inverse operations, using ticket sales for visualization, and checking solutions by substituting back into the original equation. Watch for: misunderstanding inverse operations, and ensure clarity in distinguishing between multiplication and division.

Question 18

A recipe uses 18 cups for nine servings; solve 9x=189x = 18.

  1. 2 (correct answer)
  2. 27
  3. 9
  4. 1
Explanation: This question tests middle-level algebra skills: solving one-step equations with a variable. Understanding one-step equations involves performing inverse operations to isolate the variable. For example, if 9x = 9, divide both sides by 9 to solve for x. In this specific question, the equation 9x = 18 requires dividing both sides by 9, resulting in x = 2. Choice A is correct because it accurately reflects the solution to the equation. Choice B is incorrect as it results from multiplying instead of dividing, a common mistake in recipes. To help students: Encourage practicing inverse operations, using serving sizes for visualization, and checking solutions by substituting back into the original equation. Watch for: misunderstanding inverse operations, and ensure clarity in distinguishing between multiplication and division.

Question 19

Nine trading cards cost 6363; solve 9x=639x = 63.

  1. 7 (correct answer)
  2. 72
  3. 9
  4. 54
Explanation: This question tests middle-level algebra skills: solving one-step equations with a variable. Understanding one-step equations involves performing inverse operations to isolate the variable. For example, if 9x = 18, divide both sides by 9 to solve for x. In this specific question, the equation 9x = 63 requires dividing both sides by 9, resulting in x = 7. Choice A is correct because it accurately reflects the solution to the equation. Choice D is incorrect as it results from not dividing fully, a common mistake with multiples of 9. To help students: Encourage practicing inverse operations, using trading scenarios for visualization, and checking solutions by substituting back into the original equation. Watch for: misunderstanding inverse operations, and ensure clarity in distinguishing between multiplication and division.

Question 20

A car goes 180 miles in six hours; solve 6x=1806x = 180.

  1. 30 (correct answer)
  2. 186
  3. 36
  4. 60
Explanation: This question tests middle-level algebra skills: solving one-step equations with a variable. Understanding one-step equations involves performing inverse operations to isolate the variable. For example, if 6x = 30, divide both sides by 6 to solve for x. In this specific question, the equation 6x = 180 requires dividing both sides by 6, resulting in x = 30. Choice A is correct because it accurately reflects the solution to the equation. Choice B is incorrect as it results from adding instead of dividing, a common mistake when students misapply operations. To help students: Encourage practicing inverse operations, using real-world speed contexts for visualization, and checking solutions by substituting back into the original equation. Watch for: misunderstanding inverse operations, and ensure clarity in distinguishing between multiplication and division.