How it works

A linear equation contains a variable raised only to the power of 1. To solve, use inverse operations to isolate the variable, keeping the equation balanced by doing the same operation to both sides. If the unknown appears on both sides, collect all variable terms on one side and constants on the other before dividing.

The method

1. 1.Expand any brackets
2. 2.Collect like terms, moving variables to one side and numbers to the other
3. 3.Simplify both sides
4. 4.Divide to leave the variable on its own

Worked example

Solve 3x + 7 = 22.

1. Subtract 7: 3x = 15undo addition first
2. Divide by 3: x = 5

Worked example

Solve 5x - 3 = 2x + 12.

1. Subtract 2x: 3x - 3 = 12
2. Add 3: 3x = 15
3. Divide by 3: x = 5

Common mistakes

• Not applying the same operation to both sides of the equation
• Making sign errors when moving terms across the equals sign
• Dividing only part of an expression instead of the whole side