One-Step Equations

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SSAT Middle Level: Quantitative › One-Step Equations

Questions 1 - 10
1

Four identical bracelets cost $32$; solve $4x = 32$.

8

16

28

36

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 = 16, divide both sides by 4 to solve for x. In this specific question, the equation 4x = 32 requires dividing both sides by 4, resulting in x = 8. Choice C 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 with even numbers. To help students: Encourage practicing inverse operations, using group purchases 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.

2

A group raises $96$ selling $x$ tickets at $8$ each: $8x = 96$.

12

16

88

104

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.

3

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

1

2

9

27

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.

4

Nine trading cards cost $63$; solve $9x = 63$.

7

9

54

72

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.

5

A store sells five notebooks for $25$; solve $5x = 25$.

5

20

30

125

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 5x = 10, divide both sides by 5 to solve for x. In this specific question, the equation 5x = 25 requires dividing both sides by 5, resulting in x = 5. Choice C is correct because it accurately reflects the solution to the equation. Choice D is incorrect as it results from multiplying instead of dividing, a common mistake in cost problems. To help students: Encourage practicing inverse operations, using shopping 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.

6

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

30

36

60

186

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.

7

A bus goes 240 miles in eight hours; solve $8x = 240$.

16

30

32

248

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 = 240 requires dividing both sides by 8, resulting in x = 30. 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 with large numbers. To help students: Encourage practicing inverse operations, using bus travel 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.

8

Twelve muffins share 36 strawberries; solve $12x = 36$.

3

4

24

48

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 12x = 24, divide both sides by 12 to solve for x. In this specific question, the equation 12x = 36 requires dividing both sides by 12, resulting in x = 3. Choice B is correct because it accurately reflects the solution to the equation. Choice A is incorrect as it results from not dividing properly, a common mistake when handling larger numbers. To help students: Encourage practicing inverse operations, using sharing 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.

9

Ten servings use 50 cups total; solve $10x = 50$.

5

10

40

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 10x = 20, divide both sides by 10 to solve for x. In this specific question, the equation 10x = 50 requires dividing both sides by 10, resulting in x = 5. 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 with tens. To help students: Encourage practicing inverse operations, using cup measurements 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.

10

A runner jogs 72 miles in eight hours; solve $8x = 72$.

8

9

16

64

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 = 40, divide both sides by 8 to solve for x. In this specific question, the equation 8x = 72 requires dividing both sides by 8, resulting in x = 9. 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 invert operations. To help students: Encourage practicing inverse operations, using distance and time 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.

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