An equation says two things are equal and contains an unknown letter — like 3x + 4 = 19. Solving it means being a detective: working backwards to uncover the one value of x that makes the statement true.
Why this matters: equations turn word problems into something you can actually solve — "I think of a number, times it by 3 and add 4 to get 19; what was it?" becomes 3x + 4 = 19. From working out prices and ages to rearranging science formulae, the skill of undoing operations one step at a time is one of the most reused tools in all of maths.
The golden rule: an equation is like a balanced set of scales. Whatever you do to one side, you must do to the other — then it stays perfectly level.
Undo the operations in reverse
Use inverse operations to peel away everything around x, like unwrapping a parcel from the outside in. Undo in reverse order: deal with + and − first, then × and ÷.
3x + 4 = 19:
• Subtract 4 from both sides: 3x = 15.
• Divide both sides by 3: x = 5.
Check: 3 × 5 + 4 = 19 ✓
• Subtract 4 from both sides: 3x = 15.
• Divide both sides by 3: x = 5.
Check: 3 × 5 + 4 = 19 ✓
| You see | To undo it, do the opposite |
|---|---|
| + 4 | subtract 4 |
| − 5 | add 5 |
| × 3 (i.e. 3x) | divide by 3 |
| ÷ 4 (i.e. x/4) | multiply by 4 |
Equations with brackets
If there's a bracket, expand it first (or divide both sides by the outside number), then solve as usual.
3(x + 2) = 21: divide both sides by 3 → x + 2 = 7, then subtract 2 → x = 5.
Unknowns on both sides
If x appears on both sides, first gather all the x's onto one side and all the plain numbers onto the other — then finish as normal.
5x − 2 = 2x + 10: subtract 2x from both sides → 3x − 2 = 10, add 2 → 3x = 12, divide by 3 → x = 4.
Common mistake: whatever you do, do it to the whole side. When you divide, every term must be divided — and remember to keep the balance, changing both sides identically, never just one.
In a nutshell: keep the scale balanced, undo with inverse operations working outside-in, and always substitute your answer back in to check it truly works.