What is a linear equation?
A linear equation in one variable is an equation like x + 3 = 7 or 2x − 1 = 9, where the variable appears to the first power only. The two sides are joined by an equals sign, and solving means finding the value of the variable that makes both sides equal.
The balance idea
Think of an equation as a balanced scale. Whatever you do to one side, you must do to the other so it stays balanced.
Key idea / Key idea
To keep an equation true, add, subtract, multiply or divide both sides by the same number. Undo operations to leave the variable alone.
Solving step by step
Worked example / Worked example
Solve 2x + 3 = 11.
Subtract 3 from both sides: 2x + 3 − 3 = 11 − 3, so 2x = 8.
Divide both sides by 2: x = 8 ÷ 2 = 4.
Check: 2 × 4 + 3 = 8 + 3 = 11. Correct.
Some equations need the variable collected first. For 5x − 2 = 3x + 6, subtract 3x from both sides to get 2x − 2 = 6, then add 2 to get 2x = 8, so x = 4.
Remember / Remember
- Do the same operation to both sides.
- Undo + with −, and × with ÷.
- Always check by substituting your answer back.