Solving Linear Equations Practice Worksheet

Practice solving one-step, multi-step, and variable-on-both-sides equations with step-by-step solutions.

Solve each equation before revealing the solution. Focus on showing clear algebra steps and checking your work.

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Level 1: One-Step Equations

Problem 1
\[ x + 7 = 15 \]
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Subtract \(7\) from both sides.

\[ x + 7 - 7 = 15 - 7 \] \[ x = 8 \]
Problem 2
\[ 3x = 27 \]
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Divide both sides by \(3\).

\[ \frac{3x}{3} = \frac{27}{3} \] \[ x = 9 \]
Problem 3
\[ \frac{x}{5} = 4 \]
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Multiply both sides by \(5\).

\[ 5 \cdot \frac{x}{5} = 4(5) \] \[ x = 20 \]

Level 2: Multi-Step Equations

Problem 4
\[ 2x + 5 = 19 \]
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Subtract \(5\) from both sides.

\[ 2x = 14 \]

Divide by \(2\).

\[ x = 7 \]
Problem 5
\[ 4x - 9 = 31 \]
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Add \(9\) to both sides.

\[ 4x = 40 \]

Divide by \(4\).

\[ x = 10 \]
Problem 6
\[ 5(x - 2) = 35 \]
Show solution

Divide both sides by \(5\).

\[ x - 2 = 7 \]

Add \(2\).

\[ x = 9 \]

Level 3: Variables on Both Sides

Problem 7
\[ 3x + 5 = x + 17 \]
Show solution

Subtract \(x\) from both sides.

\[ 2x + 5 = 17 \]

Subtract \(5\).

\[ 2x = 12 \] \[ x = 6 \]
Problem 8
\[ 7x - 4 = 3x + 20 \]
Show solution

Subtract \(3x\) from both sides.

\[ 4x - 4 = 20 \]

Add \(4\).

\[ 4x = 24 \] \[ x = 6 \]

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