Algebra worksheet for solving equations and inequalities with step-by-step solutions.

Let's solve each problem step by step, clearly showing all the work.

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1. Solve the following. Show all steps clearly.

a) $ x + 5 = -4 $

To isolate $ x $, subtract 5 from both sides:

$$
x + 5 - 5 = -4 - 5 \\
x = -9
$$

✔ Answer: $ x = -9 $

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b) $ r - 3 = 4 $

Add 3 to both sides:

$$
r - 3 + 3 = 4 + 3 \\
r = 7
$$

✔ Answer: $ r = 7 $

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c) $ -3 + j = 21 $

Add 3 to both sides:

$$
-3 + j + 3 = 21 + 3 \\
j = 24
$$

✔ Answer: $ j = 24 $

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d) $ 3 = n + 5 $

Subtract 5 from both sides:

$$
3 - 5 = n + 5 - 5 \\
-2 = n
$$

✔ Answer: $ n = -2 $

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2. Solve the following. Show all steps clearly.

a) $ 2j = 6 $

Divide both sides by 2:

$$
\frac{2j}{2} = \frac{6}{2} \\
j = 3
$$

✔ Answer: $ j = 3 $

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b) $ 25x = -50 $

Divide both sides by 25:

$$
\frac{25x}{25} = \frac{-50}{25} \\
x = -2
$$

✔ Answer: $ x = -2 $

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c) $ 3r = 27 $

Divide both sides by 3:

$$
\frac{3r}{3} = \frac{27}{3} \\
r = 9
$$

✔ Answer: $ r = 9 $

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d) $ 44 = -4n $

Divide both sides by -4:

$$
\frac{44}{-4} = \frac{-4n}{-4} \\
-11 = n
$$

✔ Answer: $ n = -11 $

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3. Solve the following. Show all steps clearly.

a) $ 8 = \frac{x}{4} $

Multiply both sides by 4:

$$
8 \cdot 4 = \frac{x}{4} \cdot 4 \\
32 = x
$$

✔ Answer: $ x = 32 $

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b) $ \frac{x}{2} = 4 $

Multiply both sides by 2:

$$
\frac{x}{2} \cdot 2 = 4 \cdot 2 \\
x = 8
$$

✔ Answer: $ x = 8 $

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c) $ \frac{x}{3} = 6 $

Multiply both sides by 3:

$$
\frac{x}{3} \cdot 3 = 6 \cdot 3 \\
x = 18
$$

✔ Answer: $ x = 18 $

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d) $ \frac{x}{2} = 5 $

Multiply both sides by 2:

$$
\frac{x}{2} \cdot 2 = 5 \cdot 2 \\
x = 10
$$

✔ Answer: $ x = 10 $

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4. Solve the following. Show all steps clearly.

a) $ 2x = 2 + 4x $

Subtract $ 4x $ from both sides:

$$
2x - 4x = 2 + 4x - 4x \\
-2x = 2
$$

Divide both sides by -2:

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

✔ Answer: $ x = -1 $

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b) $ 5x + 2x = 35 $

Combine like terms:

$$
7x = 35
$$

Divide by 7:

$$
x = \frac{35}{7} = 5
$$

✔ Answer: $ x = 5 $

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c) $ -3 + j = -6j + 18 $

Add $ 6j $ to both sides:

$$
-3 + j + 6j = -6j + 18 + 6j \\
-3 + 7j = 18
$$

Add 3 to both sides:

$$
7j = 18 + 3 = 21
$$

Divide by 7:

$$
j = \frac{21}{7} = 3
$$

✔ Answer: $ j = 3 $

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d) $ 6n - 10 = n + 5 $

Subtract $ n $ from both sides:

$$
6n - n - 10 = n + 5 - n \\
5n - 10 = 5
$$

Add 10 to both sides:

$$
5n = 5 + 10 = 15
$$

Divide by 5:

$$
n = \frac{15}{5} = 3
$$

✔ Answer: $ n = 3 $

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5. Solve the following. Show all steps clearly.

a) $ 2(x + 1) = -4 $

Distribute the 2:

$$
2x + 2 = -4
$$

Subtract 2 from both sides:

$$
2x = -4 - 2 = -6
$$

Divide by 2:

$$
x = \frac{-6}{2} = -3
$$

✔ Answer: $ x = -3 $

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b) $ 2(x + 4) = 14 $

Distribute:

$$
2x + 8 = 14
$$

Subtract 8:

$$
2x = 14 - 8 = 6
$$

Divide by 2:

$$
x = \frac{6}{2} = 3
$$

✔ Answer: $ x = 3 $

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c) $ 2(4x - 5) = 2x + 2 $

Distribute on left:

$$
8x - 10 = 2x + 2
$$

Subtract $ 2x $ from both sides:

$$
6x - 10 = 2
$$

Add 10:

$$
6x = 12
$$

Divide by 6:

$$
x = \frac{12}{6} = 2
$$

✔ Answer: $ x = 2 $

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d) $ 12 + x = 3(x + 2) $

Distribute on right:

$$
12 + x = 3x + 6
$$

Subtract $ x $ from both sides:

$$
12 = 2x + 6
$$

Subtract 6:

$$
6 = 2x
$$

Divide by 2:

$$
x = 3
$$

✔ Answer: $ x = 3 $

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✔ Final Answers Summary:

#### 1.
a) $ x = -9 $
b) $ r = 7 $
c) $ j = 24 $
d) $ n = -2 $

#### 2.
a) $ j = 3 $
b) $ x = -2 $
c) $ r = 9 $
d) $ n = -11 $

#### 3.
a) $ x = 32 $
b) $ x = 8 $
c) $ x = 18 $
d) $ x = 10 $

#### 4.
a) $ x = -1 $
b) $ x = 5 $
c) $ j = 3 $
d) $ n = 3 $

#### 5.
a) $ x = -3 $
b) $ x = 3 $
c) $ x = 2 $
d) $ x = 3 $

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