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Ontario MTH1W · Algebra · C1.5

Solve and verify equations

Create, solve, and check equations by keeping both sides balanced.

The core idea

An equation says two expressions are equal. Undo operations in reverse order, make the same change on both sides, and substitute your solution back into the original equation to verify it.

Learning example

Solve a two-step equation

Solve 3x − 5 = 16.

  1. 1

    Add 5 to both sides: 3x = 21.

  2. 2

    Divide both sides by 3: x = 7.

  3. 3

    Check: 3(7) − 5 = 21 − 5 = 16.

Answerx = 7

A common mistake

Moving −5 across the equals sign without understanding why its sign changes. Adding 5 to both sides makes the balance explicit.

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