How do you solve a linear equation?
Short answer
Get the unknown on its own by doing the same operation to both sides of the equation. Undo additions and subtractions first, then multiplications and divisions. For 3x + 5 = 20: subtract 5 to get 3x = 15, then divide by 3 to get x = 5.
Step by step
- Expand any brackets.
- If the unknown appears on both sides, move all the unknown terms to one side.
- Move the number terms to the other side by adding or subtracting.
- Divide both sides by the number in front of the unknown.
- Substitute your answer back into the original equation to check it.
Worked example
Solve 5x − 4 = 2x + 11
- Subtract 2x from both sides: 3x − 4 = 11
- Add 4 to both sides: 3x = 15
- Divide by 3: x = 5
- Check: 5(5) − 4 = 21 and 2(5) + 11 = 21
Common mistakes
- Doing an operation to only one side.
- Changing a sign incorrectly when moving a term.
- Multiplying only the first term inside a bracket.
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