StudyBlaze

Building a Foundation

1. What is the first step in solving the two-step equation 2x + 5 = 15? (1 choice)

Add 5 to both sides

Divide both sides by 2

Subtract 5 from both sides

Multiply both sides by 2

2. Which of the following are characteristics of a two-step equation? (multiple choice)

Always results in a fraction

Involves only one operation

Requires two operations to solve

Can be written in the form ax + b = c

3. Explain why it is important to perform the same operation on both sides of a two-step equation.

4. List the two operations typically involved in solving a two-step equation.

First operation

Second operation

Your answers will be evaluated by AI for key concepts, not exact wording. Focus on main ideas.

Understanding and Interpretation

5. In the equation 4x - 7 = 9, what is the purpose of adding 7 to both sides? (1 choice)

To check the solution

To eliminate the variable

To isolate the variable term

To simplify the equation

6. Which of the following steps are necessary to solve the equation 3x + 6 = 12? (multiple choice)

Multiply both sides by 3

Divide both sides by 3

Add 6 to both sides

Subtract 6 from both sides

7. Describe how solving a two-step equation is similar to solving a real-world problem.

Application and Analysis

8. Solve the equation 5x + 3 = 23. What is the value of x? (1 choice)

9. Which of the following equations can be solved using the two-step method? (multiple choice)

2x + 4 = 10

x/3 - 2 = 5

7x = 21

x + 3 = 6

10. Create a real-world scenario that can be modeled by the equation 2x + 5 = 15. Explain how you would solve it.

Evaluation and Creation

11. If the equation 6x - 4 = 14 is solved incorrectly as x = 3, what mistake might have been made? (1 choice)

Incorrect division

Incorrect multiplication

Incorrect subtraction

Incorrect addition

12. Analyze the equation 4x + 8 = 20. Which steps are part of the correct solution process? (multiple choice)

Add 8 to both sides

Subtract 8 from both sides

Divide both sides by 4

Multiply both sides by 4

13. Which of the following statements best evaluates the solution process for the equation 3x + 9 = 18? (1 choice)

The solution process is incorrect because it results in a negative value.

The solution process is correct because it simplifies the equation.

The solution process is correct because the operations maintain equality.

The solution process is incorrect because the wrong operations were used.

14. Design a two-step equation that represents the following scenario: "A person has $50 and spends $3 on each book they buy. How many books can they buy if they want to have $20 left?" (multiple choice)

3x + 20 = 50

3x - 50 = 20

50 - 3x = 20

20 + 3x = 50

15. Create a complex real-world problem that can be solved using a two-step equation. Provide the equation and explain the solution process.

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