Solving equations
One-step and two-step equations, and unknowns on both sides
An equation is like a balanced scale. Whatever you do to one side, you must do to the other.
Use inverse operations
To get the letter on its own, undo what has been done to it, in reverse order.
- + is undone by −, and × is undone by ÷.
- x + 7 = 12 → subtract 7 from both sides → x = 5.
- 4x = 28 → divide both sides by 4 → x = 7.
Always check by substituting your answer back in.
Worked examples
Example 1. Solve 3x + 4 = 19.
Example 2. Solve x/4 − 2 = 3.
Example 3. Solve 5x − 3 = 2x + 9.
Example 4. Solve 2(x + 3) = 16.
Top tips and common mistakes
- Write each step on a new line with the equals signs lined up.
- Answers can be negative or fractions, like x = −2 or x = 3.5.
- When x is on both sides, move the smaller x term first.
Equations are like puzzles. I love it when the check works out!
Practise
Answer as many as you like. Every question is new, and you get a “correct” tick for each one you get right first time. Use “Show answer” to see a worked solution.
Quiz: earn your stamp
Printable worksheet
Solving equations worksheet. The questions come first and the answers for grown-ups are on the last page, so you can print just the question pages.
Printing is optional. A4 size.