Math worksheet featuring eight linear equations to solve, designed for practice and learning.

Let's solve each of the linear equations step by step.

---

1. $\frac{6x + 5}{5} = 7$

Step 1: Multiply both sides by 5 to eliminate the denominator:
$$
6x + 5 = 35
$$

Step 2: Subtract 5 from both sides:
$$
6x = 30
$$

Step 3: Divide by 6:
$$
x = 5
$$

✔ Answer: $x = 5$

---

2. $9 = \frac{4x - 5}{3}$

Step 1: Multiply both sides by 3:
$$
27 = 4x - 5
$$

Step 2: Add 5 to both sides:
$$
32 = 4x
$$

Step 3: Divide by 4:
$$
x = 8
$$

✔ Answer: $x = 8$

---

3. $\frac{5x - 5}{5} = 6$

Step 1: Simplify the left side (divide numerator by 5):
$$
x - 1 = 6
$$

Step 2: Add 1 to both sides:
$$
x = 7
$$

✔ Answer: $x = 7$

---

4. $\frac{7x - 5}{5} = 6$

Step 1: Multiply both sides by 5:
$$
7x - 5 = 30
$$

Step 2: Add 5 to both sides:
$$
7x = 35
$$

Step 3: Divide by 7:
$$
x = 5
$$

✔ Answer: $x = 5$

---

5. $5 = \frac{6x + 2}{4}$

Step 1: Multiply both sides by 4:
$$
20 = 6x + 2
$$

Step 2: Subtract 2:
$$
18 = 6x
$$

Step 3: Divide by 6:
$$
x = 3
$$

✔ Answer: $x = 3$

---

6. $\frac{4x + 8}{4} = 6$

Step 1: Simplify the left side:
$$
x + 2 = 6
$$

Step 2: Subtract 2:
$$
x = 4
$$

✔ Answer: $x = 4$

---

7. $\frac{6x + 9}{3} = 13$

Step 1: Simplify the left side:
$$
2x + 3 = 13
$$

Step 2: Subtract 3:
$$
2x = 10
$$

Step 3: Divide by 2:
$$
x = 5
$$

✔ Answer: $x = 5$

---

8. $2 = \frac{3x - 2}{5}$

Step 1: Multiply both sides by 5:
$$
10 = 3x - 2
$$

Step 2: Add 2:
$$
12 = 3x
$$

Step 3: Divide by 3:
$$
x = 4
$$

✔ Answer: $x = 4$

---

✔ Final Answers:

1. $x = 5$
2. $x = 8$
3. $x = 7$
4. $x = 5$
5. $x = 3$
6. $x = 4$
7. $x = 5$
8. $x = 4$

Let me know if you'd like a visual explanation or practice problems!