Solving Linear Equations Assessments - 8.EE.7 {EDITABLE} - Free Printable

Problem: Solving Linear Equations Exam

The task involves matching terms with their correct definitions and answering multiple-choice questions related to linear equations. Below is a detailed explanation of the solution for each part.

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#### Matching Section
We need to match the following problems and terms with their correct answers:

1. Equation
- Definition: A mathematical statement that contains numbers or variables and expresses that two expressions are equal.
- Correct Answer: F

2. Like Terms
- Definition: Terms that have the same variable(s) raised to the same power(s).
- Correct Answer: C

3. Constant
- Definition: A term in an expression that does not contain any variables.
- Correct Answer: B

4. Coefficient
- Definition: The numerical factor in front of a variable in a term.
- Correct Answer: D

5. Solution
- Definition: The value(s) of the variable(s) that make the equation true.
- Correct Answer: E

6. No Solution
- Definition: A situation where no value of the variable satisfies the equation.
- Correct Answer: A

7. Infinite Solutions
- Definition: A situation where every value of the variable satisfies the equation.
- Correct Answer: G

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#### Multiple-Choice Questions

9. Which of the following is a two-step equation?
- A. \( x + 8 = 21 \)
- This is a one-step equation because it only requires subtracting 8 from both sides to solve for \( x \).
- B. \( 3x + 9 = 21 \)
- This is a two-step equation because it requires first subtracting 9 from both sides and then dividing by 3 to solve for \( x \).
- Correct Answer: B

10. Evaluate \( 5(g + 7m) \) for \( g = 4 \) and \( m = 9 \).
- Substitute \( g = 4 \) and \( m = 9 \) into the expression:
\[
5(g + 7m) = 5(4 + 7 \cdot 9)
\]
- Simplify inside the parentheses:
\[
4 + 7 \cdot 9 = 4 + 63 = 67
\]
- Multiply by 5:
\[
5 \cdot 67 = 335
\]
- Correct Answer: D

11. Which of the following equations has no solution?
- A. \( 18x + 3 = 18x + 10 \)
- Subtract \( 18x \) from both sides:
\[
3 = 10
\]
- This is a contradiction, so there is no solution.
- B. \( 8(x - 3) = 8x - 12 \)
- Distribute on the left side:
\[
8x - 24 = 8x - 12
\]
- Subtract \( 8x \) from both sides:
\[
-24 = -12
\]
- This is also a contradiction, so there is no solution.
- C. \( 3(2 + x) = 6 + 3x \)
- Distribute on the left side:
\[
6 + 3x = 6 + 3x
\]
- This is always true, so there are infinite solutions.
- Correct Answer: A or B (both have no solution, but typically only one option is marked correct; here we choose A as per the question format)

12. What is the solution of \( 4 + 2x = 4 \)?
- Subtract 4 from both sides:
\[
2x = 0
\]
- Divide by 2:
\[
x = 0
\]
- Correct Answer: C

13. Which of the following shows a simplified expression of \( 13 + 8x - 20 + 4x \)?
- Combine like terms:
\[
13 - 20 + 8x + 4x = -7 + 12x
\]
- Correct Answer: B

14. Which of the following shows like terms?
- A. \( x \) and \( 5 \)
- These are not like terms because one is a variable and the other is a constant.
- B. \( 2x \) and \( 3x \)
- These are like terms because they both have the variable \( x \) raised to the same power.
- C. \( xy \) and \( 2yz \)
- These are not like terms because they involve different variables.
- Correct Answer: B

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Final Answers:

1. Equation: F
2. Like Terms: C
3. Constant: B
4. Coefficient: D
5. Solution: E
6. No Solution: A
7. Infinite Solutions: G

Multiple-Choice:
9. B
10. D
11. A
12. C
13. B
14. B

Boxed Final Answer:
\[
\boxed{
\text{Matching: } 1-F, 2-C, 3-B, 4-D, 5-E, 6-A, 7-G \\
\text{Multiple-Choice: } 9-B, 10-D, 11-A, 12-C, 13-B, 14-B
}
\]