Two-step equations practice worksheet with step-by-step solutions for solving linear equations.

Problem Overview:

The provided images contain exercises on solving two-step equations. The tasks involve filling in blanks to solve equations and solving equations directly, with some requiring rounding of decimal answers to the hundredths place.

Solution Explanation:

#### Page 1: Two-Step Equations

##### Section 1: Fill in the blanks to solve each equation.

1. Equation: \( 6x - 18 = 33 \)
- Steps:
1. Add 18 to both sides:
\[
6x - 18 + 18 = 33 + 18
\]
Simplify:
\[
6x = 51
\]
2. Divide both sides by 6:
\[
\frac{6x}{6} = \frac{51}{6}
\]
Simplify:
\[
x = \frac{51}{6} = 8.5
\]

- Solution: \( x = 8.5 \)

2. Equation: \( \frac{2}{3}x + 4 = -2 \)
- Steps:
1. Subtract 4 from both sides:
\[
\frac{2}{3}x + 4 - 4 = -2 - 4
\]
Simplify:
\[
\frac{2}{3}x = -6
\]
2. Multiply both sides by the reciprocal of \( \frac{2}{3} \), which is \( \frac{3}{2} \):
\[
\frac{3}{2} \cdot \frac{2}{3}x = -6 \cdot \frac{3}{2}
\]
Simplify:
\[
x = -9
\]

- Solution: \( x = -9 \)

##### Section 2: Solve each equation.

1. Equation: \( -3x + 10 = 26 \)
- Steps:
1. Subtract 10 from both sides:
\[
-3x + 10 - 10 = 26 - 10
\]
Simplify:
\[
-3x = 16
\]
2. Divide both sides by -3:
\[
\frac{-3x}{-3} = \frac{16}{-3}
\]
Simplify:
\[
x = -\frac{16}{3} \approx -5.33
\]

- Solution: \( x = -\frac{16}{3} \) or \( -5.33 \)

2. Equation: \( \frac{1}{2}x - 12 = 42 \)
- Steps:
1. Add 12 to both sides:
\[
\frac{1}{2}x - 12 + 12 = 42 + 12
\]
Simplify:
\[
\frac{1}{2}x = 54
\]
2. Multiply both sides by 2 (the reciprocal of \( \frac{1}{2} \)):
\[
2 \cdot \frac{1}{2}x = 54 \cdot 2
\]
Simplify:
\[
x = 108
\]

- Solution: \( x = 108 \)

3. Equation: \( \frac{x}{8} + 15 = 35 \)
- Steps:
1. Subtract 15 from both sides:
\[
\frac{x}{8} + 15 - 15 = 35 - 15
\]
Simplify:
\[
\frac{x}{8} = 20
\]
2. Multiply both sides by 8:
\[
8 \cdot \frac{x}{8} = 20 \cdot 8
\]
Simplify:
\[
x = 160
\]

- Solution: \( x = 160 \)

4. Equation: \( \frac{3}{4}y + 2 = -23 \)
- Steps:
1. Subtract 2 from both sides:
\[
\frac{3}{4}y + 2 - 2 = -23 - 2
\]
Simplify:
\[
\frac{3}{4}y = -25
\]
2. Multiply both sides by the reciprocal of \( \frac{3}{4} \), which is \( \frac{4}{3} \):
\[
\frac{4}{3} \cdot \frac{3}{4}y = -25 \cdot \frac{4}{3}
\]
Simplify:
\[
y = -\frac{100}{3} \approx -33.33
\]

- Solution: \( y = -\frac{100}{3} \) or \( -33.33 \)

---

#### Page 2: Solving Equations

##### Section 3: Solve each equation. Round all decimal answers to the hundredths place.

1. Equation: \( -2.1x + 8.2 = 20 \)
- Steps:
1. Subtract 8.2 from both sides:
\[
-2.1x + 8.2 - 8.2 = 20 - 8.2
\]
Simplify:
\[
-2.1x = 11.8
\]
2. Divide both sides by -2.1:
\[
\frac{-2.1x}{-2.1} = \frac{11.8}{-2.1}
\]
Simplify:
\[
x = -5.62
\]

- Solution: \( x = -5.62 \)

2. Equation: \( \frac{1}{2}x - \frac{3}{4} = -4 \frac{3}{4} \)
- Steps:
1. Add \( \frac{3}{4} \) to both sides:
\[
\frac{1}{2}x - \frac{3}{4} + \frac{3}{4} = -4 \frac{3}{4} + \frac{3}{4}
\]
Simplify:
\[
\frac{1}{2}x = -4
\]
2. Multiply both sides by 2 (the reciprocal of \( \frac{1}{2} \)):
\[
2 \cdot \frac{1}{2}x = -4 \cdot 2
\]
Simplify:
\[
x = -8
\]

- Solution: \( x = -8 \)

3. Equation: \( \frac{x}{5.5} + 15 = -65 \)
- Steps:
1. Subtract 15 from both sides:
\[
\frac{x}{5.5} + 15 - 15 = -65 - 15
\]
Simplify:
\[
\frac{x}{5.5} = -80
\]
2. Multiply both sides by 5.5:
\[
5.5 \cdot \frac{x}{5.5} = -80 \cdot 5.5
\]
Simplify:
\[
x = -440
\]

- Solution: \( x = -440 \)

4. Equation: \( -4.15x + 9 = -21.5 \)
- Steps:
1. Subtract 9 from both sides:
\[
-4.15x + 9 - 9 = -21.5 - 9
\]
Simplify:
\[
-4.15x = -30.5
\]
2. Divide both sides by -4.15:
\[
\frac{-4.15x}{-4.15} = \frac{-30.5}{-4.15}
\]
Simplify:
\[
x = 7.35
\]

- Solution: \( x = 7.35 \)

5. Equation: \( \frac{3}{5}x - 5 = \frac{6}{5} \)
- Steps:
1. Add 5 to both sides:
\[
\frac{3}{5}x - 5 + 5 = \frac{6}{5} + 5
\]
Simplify:
\[
\frac{3}{5}x = \frac{6}{5} + \frac{25}{5} = \frac{31}{5}
\]
2. Multiply both sides by the reciprocal of \( \frac{3}{5} \), which is \( \frac{5}{3} \):
\[
\frac{5}{3} \cdot \frac{3}{5}x = \frac{31}{5} \cdot \frac{5}{3}
\]
Simplify:
\[
x = \frac{31}{3} \approx 10.33
\]

- Solution: \( x = \frac{31}{3} \) or \( 10.33 \)

6. Equation: \( \frac{x}{12} - 22.8 = -14.25 \)
- Steps:
1. Add 22.8 to both sides:
\[
\frac{x}{12} - 22.8 + 22.8 = -14.25 + 22.8
\]
Simplify:
\[
\frac{x}{12} = 8.55
\]
2. Multiply both sides by 12:
\[
12 \cdot \frac{x}{12} = 8.55 \cdot 12
\]
Simplify:
\[
x = 102.6
\]

- Solution: \( x = 102.6 \)

---

Final Answers:

- Page 1:
1. \( x = 8.5 \)
2. \( x = -9 \)
3. \( x = -\frac{16}{3} \) or \( -5.33 \)
4. \( x = 108 \)
5. \( x = 160 \)
6. \( y = -\frac{100}{3} \) or \( -33.33 \)

- Page 2:
1. \( x = -5.62 \)
2. \( x = -8 \)
3. \( x = -440 \)
4. \( x = 7.35 \)
5. \( x = \frac{31}{3} \) or \( 10.33 \)
6. \( x = 102.6 \)

Boxed Final Answer:
\[
\boxed{
\begin{aligned}
&\text{Page 1: } 8.5, -9, -5.33, 108, 160, -33.33 \\
&\text{Page 2: } -5.62, -8, -440, 7.35, 10.33, 102.6
\end{aligned}
}
\]