Math worksheet for solving linear equations, featuring ten problems with variables on both sides, suitable for classroom use.

Problem: Solve the Equations

We are tasked with solving a set of linear equations. Each equation will be solved step by step, and the solutions will be rounded to the nearest hundredth if necessary.

---

#### Equation 1: $ -4k + 3 = -9 - 7k $

1. Add $ 7k $ to both sides:
$$
-4k + 7k + 3 = -9
$$
$$
3k + 3 = -9
$$

2. Subtract 3 from both sides:
$$
3k = -9 - 3
$$
$$
3k = -12
$$

3. Divide both sides by 3:
$$
k = \frac{-12}{3}
$$
$$
k = -4
$$

Solution: $ k = -4 $

---

#### Equation 2: $ -5 + 3r = -2 - 3(9 + 4r) $

1. Distribute the $-3$ on the right-hand side:
$$
-5 + 3r = -2 - 27 - 12r
$$
$$
-5 + 3r = -29 - 12r
$$

2. Add $ 12r $ to both sides:
$$
-5 + 3r + 12r = -29
$$
$$
-5 + 15r = -29
$$

3. Add 5 to both sides:
$$
15r = -29 + 5
$$
$$
15r = -24
$$

4. Divide both sides by 15:
$$
r = \frac{-24}{15}
$$
$$
r = -1.6
$$

Solution: $ r = -1.6 $

---

#### Equation 3: $ -6 - 4x = 4x + 5x $

1. Combine like terms on the right-hand side:
$$
-6 - 4x = 9x
$$

2. Add $ 4x $ to both sides:
$$
-6 = 9x + 4x
$$
$$
-6 = 13x
$$

3. Divide both sides by 13:
$$
x = \frac{-6}{13}
$$
$$
x \approx -0.46
$$

Solution: $ x \approx -0.46 $

---

#### Equation 4: $ -3s - 9 = 7(-3s + 4) $

1. Distribute the 7 on the right-hand side:
$$
-3s - 9 = -21s + 28
$$

2. Add $ 21s $ to both sides:
$$
-3s + 21s - 9 = 28
$$
$$
18s - 9 = 28
$$

3. Add 9 to both sides:
$$
18s = 28 + 9
$$
$$
18s = 37
$$

4. Divide both sides by 18:
$$
s = \frac{37}{18}
$$
$$
s \approx 2.06
$$

Solution: $ s \approx 2.06 $

---

#### Equation 5: $ -2f - 4f - 8 = -3f + 9 $

1. Combine like terms on the left-hand side:
$$
-6f - 8 = -3f + 9
$$

2. Add $ 3f $ to both sides:
$$
-6f + 3f - 8 = 9
$$
$$
-3f - 8 = 9
$$

3. Add 8 to both sides:
$$
-3f = 9 + 8
$$
$$
-3f = 17
$$

4. Divide both sides by $-3$:
$$
f = \frac{17}{-3}
$$
$$
f \approx -5.67
$$

Solution: $ f \approx -5.67 $

---

#### Equation 6: $ -5(-9 - 5d) = 9(6d - 3) $

1. Distribute on both sides:
$$
45 + 25d = 54d - 27
$$

2. Subtract $ 54d $ from both sides:
$$
45 + 25d - 54d = -27
$$
$$
45 - 29d = -27
$$

3. Subtract 45 from both sides:
$$
-29d = -27 - 45
$$
$$
-29d = -72
$$

4. Divide both sides by $-29$:
$$
d = \frac{-72}{-29}
$$
$$
d \approx 2.48
$$

Solution: $ d \approx 2.48 $

---

#### Equation 7: $ 3h + 5(-9 - 5h) = -3h + 2h $

1. Distribute the 5 on the left-hand side:
$$
3h - 45 - 25h = -3h + 2h
$$

2. Combine like terms on both sides:
$$
-22h - 45 = -h
$$

3. Add $ h $ to both sides:
$$
-22h + h - 45 = 0
$$
$$
-21h - 45 = 0
$$

4. Add 45 to both sides:
$$
-21h = 45
$$

5. Divide both sides by $-21$:
$$
h = \frac{45}{-21}
$$
$$
h \approx -2.14
$$

Solution: $ h \approx -2.14 $

---

#### Equation 8: $ -2 + 5v = 3(v - 5) $

1. Distribute the 3 on the right-hand side:
$$
-2 + 5v = 3v - 15
$$

2. Subtract $ 3v $ from both sides:
$$
-2 + 5v - 3v = -15
$$
$$
-2 + 2v = -15
$$

3. Add 2 to both sides:
$$
2v = -15 + 2
$$
$$
2v = -13
$$

4. Divide both sides by 2:
$$
v = \frac{-13}{2}
$$
$$
v = -6.5
$$

Solution: $ v = -6.5 $

---

#### Equation 9: $ 9(y + 2) - 5(y - 6) = -4y - 9 $

1. Distribute on both sides:
$$
9y + 18 - 5y + 30 = -4y - 9
$$

2. Combine like terms:
$$
4y + 48 = -4y - 9
$$

3. Add $ 4y $ to both sides:
$$
4y + 4y + 48 = -9
$$
$$
8y + 48 = -9
$$

4. Subtract 48 from both sides:
$$
8y = -9 - 48
$$
$$
8y = -57
$$

5. Divide both sides by 8:
$$
y = \frac{-57}{8}
$$
$$
y \approx -7.12
$$

Solution: $ y \approx -7.12 $

---

#### Equation 10: $ 9 + 5n - 4 + 5 = 4n - -2 $

1. Simplify both sides:
$$
9 - 4 + 5 + 5n = 4n + 2
$$
$$
10 + 5n = 4n + 2
$$

2. Subtract $ 4n $ from both sides:
$$
10 + 5n - 4n = 2
$$
$$
10 + n = 2
$$

3. Subtract 10 from both sides:
$$
n = 2 - 10
$$
$$
n = -8
$$

Solution: $ n = -8 $

---

Final Answers:

$$
\boxed{
\begin{aligned}
1) & \quad k = -4 \\
2) & \quad r = -1.6 \\
3) & \quad x \approx -0.46 \\
4) & \quad s \approx 2.06 \\
5) & \quad f \approx -5.67 \\
6) & \quad d \approx 2.48 \\
7) & \quad h \approx -2.14 \\
8) & \quad v = -6.5 \\
9) & \quad y \approx -7.12 \\
10) & \quad n = -8
\end{aligned}
}
$$