Practice worksheet for solving equations with variables on both sides, designed for math education.

Problem: Solve each equation for \( x \).

We will solve each equation step by step. The goal is to isolate \( x \) on one side of the equation.

---

#### 1. \( 4x - 19 = x + 11 \)

1. Subtract \( x \) from both sides:
\[
4x - x - 19 = x - x + 11
\]
\[
3x - 19 = 11
\]

2. Add 19 to both sides:
\[
3x - 19 + 19 = 11 + 19
\]
\[
3x = 30
\]

3. Divide both sides by 3:
\[
\frac{3x}{3} = \frac{30}{3}
\]
\[
x = 10
\]

Solution: \( x = 10 \)

---

#### 2. \( 2x - 3 = 11x - 21 \)

1. Subtract \( 2x \) from both sides:
\[
2x - 2x - 3 = 11x - 2x - 21
\]
\[
-3 = 9x - 21
\]

2. Add 21 to both sides:
\[
-3 + 21 = 9x - 21 + 21
\]
\[
18 = 9x
\]

3. Divide both sides by 9:
\[
\frac{18}{9} = \frac{9x}{9}
\]
\[
x = 2
\]

Solution: \( x = 2 \)

---

#### 3. \( -22 - x = 10 - 3x \)

1. Add \( 3x \) to both sides:
\[
-22 - x + 3x = 10 - 3x + 3x
\]
\[
-22 + 2x = 10
\]

2. Add 22 to both sides:
\[
-22 + 22 + 2x = 10 + 22
\]
\[
2x = 32
\]

3. Divide both sides by 2:
\[
\frac{2x}{2} = \frac{32}{2}
\]
\[
x = 16
\]

Solution: \( x = 16 \)

---

#### 4. \( 22 + x = -x - 46 \)

1. Add \( x \) to both sides:
\[
22 + x + x = -x + x - 46
\]
\[
22 + 2x = -46
\]

2. Subtract 22 from both sides:
\[
22 - 22 + 2x = -46 - 22
\]
\[
2x = -68
\]

3. Divide both sides by 2:
\[
\frac{2x}{2} = \frac{-68}{2}
\]
\[
x = -34
\]

Solution: \( x = -34 \)

---

#### 5. \( 3x - 53 = 5x + 13 \)

1. Subtract \( 3x \) from both sides:
\[
3x - 3x - 53 = 5x - 3x + 13
\]
\[
-53 = 2x + 13
\]

2. Subtract 13 from both sides:
\[
-53 - 13 = 2x + 13 - 13
\]
\[
-66 = 2x
\]

3. Divide both sides by 2:
\[
\frac{-66}{2} = \frac{2x}{2}
\]
\[
x = -33
\]

Solution: \( x = -33 \)

---

#### 6. \( 55x + 19 = -5x - 41 \)

1. Add \( 5x \) to both sides:
\[
55x + 5x + 19 = -5x + 5x - 41
\]
\[
60x + 19 = -41
\]

2. Subtract 19 from both sides:
\[
60x + 19 - 19 = -41 - 19
\]
\[
60x = -60
\]

3. Divide both sides by 60:
\[
\frac{60x}{60} = \frac{-60}{60}
\]
\[
x = -1
\]

Solution: \( x = -1 \)

---

#### 7. \( 4 - 8x = -1 - 3x \)

1. Add \( 8x \) to both sides:
\[
4 - 8x + 8x = -1 - 3x + 8x
\]
\[
4 = -1 + 5x
\]

2. Add 1 to both sides:
\[
4 + 1 = -1 + 1 + 5x
\]
\[
5 = 5x
\]

3. Divide both sides by 5:
\[
\frac{5}{5} = \frac{5x}{5}
\]
\[
x = 1
\]

Solution: \( x = 1 \)

---

#### 8. \( 29 - x = x - 19 \)

1. Add \( x \) to both sides:
\[
29 - x + x = x + x - 19
\]
\[
29 = 2x - 19
\]

2. Add 19 to both sides:
\[
29 + 19 = 2x - 19 + 19
\]
\[
48 = 2x
\]

3. Divide both sides by 2:
\[
\frac{48}{2} = \frac{2x}{2}
\]
\[
x = 24
\]

Solution: \( x = 24 \)

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Final Answers:

\[
\boxed{10, 2, 16, -34, -33, -1, 1, 24}
\]