Sample page from a 26-question quiz focusing on solving linear equations with one variable, designed for classroom assessment.

Problem: Solve the given linear equations and select the correct answer from the provided options.

#### Step-by-Step Solution:

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Question 1: Solve the linear equation \( x - 15 = -19 \)

1. Start with the equation:
\[
x - 15 = -19
\]

2. To isolate \( x \), add 15 to both sides of the equation:
\[
x - 15 + 15 = -19 + 15
\]

3. Simplify:
\[
x = -4
\]

4. The solution is:
\[
x = -4
\]

5. Match the solution with the given options:
- A: \( x = 34 \)
- B: \( x = -34 \)
- C: \( x = -4 \)
- D: \( x = 4 \)

The correct answer is C.

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Question 2: Solve the linear equation \( -12y = 108 \)

1. Start with the equation:
\[
-12y = 108
\]

2. To isolate \( y \), divide both sides by \(-12\):
\[
y = \frac{108}{-12}
\]

3. Simplify the division:
\[
y = -9
\]

4. The solution is:
\[
y = -9
\]

5. Match the solution with the given options:
- A: \( y = -120 \)
- B: \( y = -9 \)
- C: \( y = 9 \)
- D: \( y = 120 \)

The correct answer is B.

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Question 3: Solve the linear equation \( \frac{x}{7} = -8 \)

1. Start with the equation:
\[
\frac{x}{7} = -8
\]

2. To isolate \( x \), multiply both sides by 7:
\[
x = -8 \times 7
\]

3. Simplify the multiplication:
\[
x = -56
\]

4. The solution is:
\[
x = -56
\]

5. Match the solution with the given options:
- A: \( x = -56 \)
- B: \( x = -15 \)
- C: \( x = 56 \)
- D: \( x = 15 \)

The correct answer is A.

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Question 4: Solve the linear equation \( \frac{x}{7} = -8 \)

1. Start with the equation:
\[
\frac{x}{7} = -8
\]

2. To isolate \( x \), multiply both sides by 7:
\[
x = -8 \times 7
\]

3. Simplify the multiplication:
\[
x = -56
\]

4. The solution is:
\[
x = -56
\]

5. Match the solution with the given options:
- A: \( x = 56 \)
- B: \( x = -56 \)
- C: \( x = -15 \)
- D: \( x = 15 \)

The correct answer is B.

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Question 5: Solve the linear equation \( \frac{3}{4}x = 27 \)

1. Start with the equation:
\[
\frac{3}{4}x = 27
\]

2. To isolate \( x \), multiply both sides by the reciprocal of \( \frac{3}{4} \), which is \( \frac{4}{3} \):
\[
x = 27 \times \frac{4}{3}
\]

3. Simplify the multiplication:
\[
x = \frac{27 \times 4}{3} = \frac{108}{3} = 36
\]

4. The solution is:
\[
x = 36
\]

5. Match the solution with the given options:
- A: \( x = -20 \frac{1}{4} \)
- B: \( x = 20 \frac{1}{4} \)

Note: The options provided do not match the solution. However, if we assume a typo in the options, the correct answer should be \( x = 36 \).

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