One-Step Equations

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SSAT Middle Level: Quantitative › One-Step Equations

Questions 1 - 10
1

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.

2

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.

3

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.

4

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.

5

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.

6

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.

7

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.

8

A team earns $84$ from $x$ tickets at $7$ each: $7x = 84$.

12

14

77

91

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 7x = 14, divide both sides by 7 to solve for x. In this specific question, the equation 7x = 84 requires dividing both sides by 7, resulting in x = 12. Choice C 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 team earnings. To help students: Encourage practicing inverse operations, using ticket earnings 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

A club earns $45$ from $x$ tickets at $9$ each: $9x = 45$.

4

5

36

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 = 9, divide both sides by 9 to solve for x. In this specific question, the equation 9x = 45 requires dividing both sides by 9, resulting in x = 5. Choice C 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 with 9s. To help students: Encourage practicing inverse operations, using earnings 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.

10

Six identical water bottles cost $42$; solve $6x = 42$.

6

7

36

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 6x = 12, divide both sides by 6 to solve for x. In this specific question, the equation 6x = 42 requires dividing both sides by 6, resulting in x = 7. 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 in costs. To help students: Encourage practicing inverse operations, using bottle 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.

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