50+ Linear Equations worksheets for 2nd Year on Quizizz | Free ... - Free Printable

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

#### Question 1: Solve \( 7x - 3x - 8 = 24 \)

1. Simplify the equation:
\[
7x - 3x - 8 = 24
\]
Combine like terms:
\[
4x - 8 = 24
\]

2. Isolate the term with \( x \):
\[
4x - 8 + 8 = 24 + 8
\]
\[
4x = 32
\]

3. Solve for \( x \):
\[
x = \frac{32}{4}
\]
\[
x = 8
\]

Correct Answer: D (8)

---

#### Question 2: Solve \( 3(x - 2) = 18 \)

1. Distribute the 3:
\[
3(x - 2) = 18
\]
\[
3x - 6 = 18
\]

2. Isolate the term with \( x \):
\[
3x - 6 + 6 = 18 + 6
\]
\[
3x = 24
\]

3. Solve for \( x \):
\[
x = \frac{24}{3}
\]
\[
x = 8
\]

Correct Answer: B (8)

---

#### Question 3: Solve \( 7x + 19 = -2x + 55 \)

1. Combine like terms by moving all \( x \)-terms to one side and constants to the other:
\[
7x + 19 = -2x + 55
\]
Add \( 2x \) to both sides:
\[
7x + 2x + 19 = 55
\]
\[
9x + 19 = 55
\]

2. Isolate the term with \( x \):
\[
9x + 19 - 19 = 55 - 19
\]
\[
9x = 36
\]

3. Solve for \( x \):
\[
x = \frac{36}{9}
\]
\[
x = 4
\]

Correct Answer: D (4)

---

#### Question 4: Solve \( 2(2x + 3) = -6(x + 9) \)

1. Distribute on both sides:
\[
2(2x + 3) = -6(x + 9)
\]
\[
4x + 6 = -6x - 54
\]

2. Combine like terms by moving all \( x \)-terms to one side and constants to the other:
\[
4x + 6 = -6x - 54
\]
Add \( 6x \) to both sides:
\[
4x + 6x + 6 = -54
\]
\[
10x + 6 = -54
\]

3. Isolate the term with \( x \):
\[
10x + 6 - 6 = -54 - 6
\]
\[
10x = -60
\]

4. Solve for \( x \):
\[
x = \frac{-60}{10}
\]
\[
x = -6
\]

Correct Answer: D (-6)

---

#### Question 5: Solve for \( x \): \( 6(2x + 1) = 18 \)

1. Distribute the 6:
\[
6(2x + 1) = 18
\]
\[
12x + 6 = 18
\]

2. Isolate the term with \( x \):
\[
12x + 6 - 6 = 18 - 6
\]
\[
12x = 12
\]

3. Solve for \( x \):
\[
x = \frac{12}{12}
\]
\[
x = 1
\]

Correct Answer: C (1)

---

#### Question 6: Solve for \( x \): \( 8x + 2 + 3x + 5 = x + 12 \)

1. Combine like terms on both sides:
\[
8x + 3x + 2 + 5 = x + 12
\]
\[
11x + 7 = x + 12
\]

2. Move all \( x \)-terms to one side and constants to the other:
\[
11x + 7 = x + 12
\]
Subtract \( x \) from both sides:
\[
11x - x + 7 = 12
\]
\[
10x + 7 = 12
\]

3. Isolate the term with \( x \):
\[
10x + 7 - 7 = 12 - 7
\]
\[
10x = 5
\]

4. Solve for \( x \):
\[
x = \frac{5}{10}
\]
\[
x = 0.5
\]

Correct Answer: Not listed (Note: The options provided do not include 0.5, so there might be an error in the options.)

---

Final Answers:

1. D (8)
2. B (8)
3. D (4)
4. D (-6)
5. C (1)
6. Not listed (0.5)

\boxed{D, B, D, D, C, \text{Not listed}}