Linear equations worksheet for solving variables with various algebraic expressions.

Let's solve each of these linear equations step by step. The goal is to solve for the variable in each equation.

---

1.

$$
\frac{16}{u} + 8 = 10
$$

Step 1: Subtract 8 from both sides:
$$
\frac{16}{u} = 2
$$

Step 2: Multiply both sides by $ u $:
$$
16 = 2u
$$

Step 3: Divide by 2:
$$
u = 8
$$

✔ Answer: $ u = 8 $

---

2.

$$
\frac{48}{y} + 5 = 13
$$

Step 1: Subtract 5:
$$
\frac{48}{y} = 8
$$

Step 2: Multiply both sides by $ y $:
$$
48 = 8y
$$

Step 3: Divide by 8:
$$
y = 6
$$

✔ Answer: $ y = 6 $

---

3.

$$
10 + \frac{20}{a} = 14
$$

Step 1: Subtract 10:
$$
\frac{20}{a} = 4
$$

Step 2: Multiply by $ a $:
$$
20 = 4a
$$

Step 3: Divide by 4:
$$
a = 5
$$

✔ Answer: $ a = 5 $

---

4.

$$
\frac{72}{a} - 8 = 0
$$

Step 1: Add 8:
$$
\frac{72}{a} = 8
$$

Step 2: Multiply by $ a $:
$$
72 = 8a
$$

Step 3: Divide by 8:
$$
a = 9
$$

✔ Answer: $ a = 9 $

---

5.

$$
4 + \frac{10}{a} = 9
$$

Step 1: Subtract 4:
$$
\frac{10}{a} = 5
$$

Step 2: Multiply by $ a $:
$$
10 = 5a
$$

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

✔ Answer: $ a = 2 $

---

6.

$$
9 + \frac{63}{c} = 16
$$

Step 1: Subtract 9:
$$
\frac{63}{c} = 7
$$

Step 2: Multiply by $ c $:
$$
63 = 7c
$$

Step 3: Divide by 7:
$$
c = 9
$$

✔ Answer: $ c = 9 $

---

7.

$$
7 + \frac{56}{v} = 15
$$

Step 1: Subtract 7:
$$
\frac{56}{v} = 8
$$

Step 2: Multiply by $ v $:
$$
56 = 8v
$$

Step 3: Divide by 8:
$$
v = 7
$$

✔ Answer: $ v = 7 $

---

8.

$$
10 + \frac{24}{x} = 13
$$

Step 1: Subtract 10:
$$
\frac{24}{x} = 3
$$

Step 2: Multiply by $ x $:
$$
24 = 3x
$$

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

✔ Answer: $ x = 8 $

---

9.

$$
\frac{16}{a} + 4 = 8
$$

Step 1: Subtract 4:
$$
\frac{16}{a} = 4
$$

Step 2: Multiply by $ a $:
$$
16 = 4a
$$

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

✔ Answer: $ a = 4 $

---

10.

$$
2 + \frac{6}{u} = 8
$$

Step 1: Subtract 2:
$$
\frac{6}{u} = 6
$$

Step 2: Multiply by $ u $:
$$
6 = 6u
$$

Step 3: Divide by 6:
$$
u = 1
$$

✔ Answer: $ u = 1 $

---

11.

$$
7 + \frac{6}{y} = 13
$$

Step 1: Subtract 7:
$$
\frac{6}{y} = 6
$$

Step 2: Multiply by $ y $:
$$
6 = 6y
$$

Step 3: Divide by 6:
$$
y = 1
$$

✔ Answer: $ y = 1 $

---

12.

$$
\frac{12}{x} - 2 = 1
$$

Step 1: Add 2:
$$
\frac{12}{x} = 3
$$

Step 2: Multiply by $ x $:
$$
12 = 3x
$$

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

✔ Answer: $ x = 4 $

---

13.

$$
2 + \frac{36}{y} = 8
$$

Step 1: Subtract 2:
$$
\frac{36}{y} = 6
$$

Step 2: Multiply by $ y $:
$$
36 = 6y
$$

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

✔ Answer: $ y = 6 $

---

14.

$$
5 + \frac{20}{u} = 7
$$

Step 1: Subtract 5:
$$
\frac{20}{u} = 2
$$

Step 2: Multiply by $ u $:
$$
20 = 2u
$$

Step 3: Divide by 2:
$$
u = 10
$$

✔ Answer: $ u = 10 $

---

15.

$$
\frac{24}{z} - 2 = 1
$$

Step 1: Add 2:
$$
\frac{24}{z} = 3
$$

Step 2: Multiply by $ z $:
$$
24 = 3z
$$

Step 3: Divide by 3:
$$
z = 8
$$

✔ Answer: $ z = 8 $

---

✔ Final Answers Summary:

| Equation | Variable | Solution |
|--------|--------|---------|
| 1 | $ u $ | 8 |
| 2 | $ y $ | 6 |
| 3 | $ a $ | 5 |
| 4 | $ a $ | 9 |
| 5 | $ a $ | 2 |
| 6 | $ c $ | 9 |
| 7 | $ v $ | 7 |
| 8 | $ x $ | 8 |
| 9 | $ a $ | 4 |
| 10 | $ u $ | 1 |
| 11 | $ y $ | 1 |
| 12 | $ x $ | 4 |
| 13 | $ y $ | 6 |
| 14 | $ u $ | 10 |
| 15 | $ z $ | 8 |

> ⚠️ Note: Some variables (like $ a $, $ u $, $ y $) appear multiple times with different values — this is fine because they are independent equations.

Let me know if you'd like this formatted as a printable answer sheet!