Question

Multi Step Equations Unit Test practice U8 L10

Answer 1

Certainly! Here are some practice problems that focus on solving multi-step equations, similar to what you might encounter in a Unit Test for a math unit on this topic.

### Practice Problems:

1. Solve for \( x \):
\[
3(x + 4) - 2 = 16
\]

2. Solve for \( y \):
\[
5y - 3(2y - 4) = 8
\]

3. Solve for \( z \):
\[
2(z - 1) + 3(2z + 4) = 26
\]

4. Solve for \( a \):
\[
4(a + 3) - 2(a - 1) = 20
\]

5. Solve for \( b \):
\[
\frac{3b + 2}{4} - 1 = 2
\]

6. Solve for \( c \):
\[
7(c + 1) - 3(2c - 5) = 22
\]

7. Solve for \( d \):
\[
6(d - 2) + 4 = 2d + 10
\]

8. Solve for \( e \):
\[
2(3e + 4) = 5(e + 2) + 2
\]

### Solutions

Here are the solutions to the practice problems:

1. **Problem**: \( 3(x + 4) - 2 = 16 \)
**Solution**:
\[
3x + 12 - 2 = 16 \\
3x + 10 = 16 \\
3x = 6 \\
x = 2
\]

2. **Problem**: \( 5y - 3(2y - 4) = 8 \)
**Solution**:
\[
5y - 6y + 12 = 8 \\
-y + 12 = 8 \\
-y = -4 \\
y = 4
\]

3. **Problem**: \( 2(z - 1) + 3(2z + 4) = 26 \)
**Solution**:
\[
2z - 2 + 6z + 12 = 26 \\
8z + 10 = 26 \\
8z = 16 \\
z = 2
\]

4. **Problem**: \( 4(a + 3) - 2(a - 1) = 20 \)
**Solution**:
\[
4a + 12 - 2a + 2 = 20 \\
2a + 14 = 20 \\
2a = 6 \\
a = 3
\]

5. **Problem**: \( \frac{3b + 2}{4} - 1 = 2 \)
**Solution**:
\[
\frac{3b + 2}{4} = 3 \\
3b + 2 = 12 \\
3b = 10 \\
b = \frac{10}{3} \text{ or } 3 \frac{1}{3}
\]

6. **Problem**: \( 7(c + 1) - 3(2c - 5) = 22 \)
**Solution**:
\[
7c + 7 - 6c + 15 = 22 \\
c + 22 = 22 \\
c = 0
\]

7. **Problem**: \( 6(d - 2) + 4 = 2d + 10 \)
**Solution**:
\[
6d - 12 + 4 = 2d + 10 \\
6d - 8 = 2d + 10 \\
4d = 18 \\
d = \frac{9}{2} \text{ or } 4.5
\]

8. **Problem**: \( 2(3e + 4) = 5(e + 2) + 2 \)
**Solution**:
\[
6e + 8 = 5e + 10 + 2 \\
6e + 8 = 5e + 12 \\
e = 4
\]

Feel free to reach out if you have any questions on these problems or if you need further assistance!