Solving Linear Equations

A linear equation contains a variable raised to the power of 1 (no x², x³, etc.). Solving means finding the value of the unknown that makes the equation true. This lesson covers one-step, two-step, and multi-step equations, including those with unknowns on both sides, brackets, and fractions.

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Key Vocabulary

Term	Meaning
Equation	A mathematical statement with an equals sign
Solution	The value of the variable that makes the equation true
Inverse operation	The opposite operation (+ undone by −; × undone by ÷)
Balancing	Doing the same thing to both sides of the equation

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One-Step Equations

Use a single inverse operation.

Worked Example 1

Solve: x + 7 = 12

x = 12 − 7 = 5

Worked Example 2

Solve: 3x = 21

x = 21 ÷ 3 = 7

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Two-Step Equations

Apply inverse operations in reverse order (undo the last operation first, or work to isolate the variable).

Worked Example 3

Solve: 2x + 5 = 17

Step 1: 2x = 17 − 5 = 12