Solving linear equations
Use inverse operations to isolate the variable. The balance method preserves equality.
Solving means finding the value of the variable that makes the equation true. Always do the same operation to both sides — the ‘balance method’. Aim: variable alone on one side.
Worked examples
3x + 5 = 17 ⇒ x = 4. Subtract 5 (12), divide by 3 (4).
2(x + 3) = 14 ⇒ x = 4. Expand or divide first.
5x − 1 = 2x + 8 ⇒ x = 3. Variables on one side, numbers on the other.
Frequently asked questions
Variables on both sides?
Subtract the smaller variable term from both sides first to keep things positive.
Always check?
Yes — substitute back into the original equation. 3(4)+5 = 17.