To solve an equation with brackets, expand every bracket first, collect the x terms on one side and the numbers on the other, then divide. This appears in almost every algebra paper, both as a direct “solve” question and as a step inside longer problems.
It builds on algebraic structure and is the first lesson in equations and formulas.
What is the idea behind it?
An equation is a balance. Whatever you do to one side, you must do to the other. Brackets only hide a multiplication: 3(2x − 5) means 3 × 2x and 3 × (−5), so it becomes 6x − 15.
The sign of the number outside the bracket travels with it. A minus in front of a bracket changes every sign inside.
How to solve it, step by step
- Expand each bracket, multiplying the outside number by every term inside.
- Simplify each side by collecting like terms.
- Move x terms to one side, choosing the side that keeps the x coefficient positive.
- Move the numbers to the other side.
- Divide by the coefficient of x.
- Check by putting your answer back into the original equation.
Worked example
Solve 3(2x − 5) = 4(x + 1) + 7
Step 1, expand: the left side is 6x − 15. The right side is 4x + 4 + 7.
Step 2, simplify: 6x − 15 = 4x + 11.
Step 3, x terms together: subtract 4x from both sides: 2x − 15 = 11.
Step 4, numbers together: add 15 to both sides: 2x = 26.
Step 5, divide: x = 13.
Check: left side 3(2 × 13 − 5) = 3 × 21 = 63. Right side 4(13 + 1) + 7 = 56 + 7 = 63. Both equal 63.
The mistake to watch for
The usual slip is expanding only the first term of the bracket.
Mistaken working: 3(2x − 5) = 6x − 5, giving 6x − 5 = 4x + 11, so 2x = 16 and x = 8.
The student multiplied 2x by 3 but forgot to multiply −5 by 3.
The check exposes it straight away: with x = 8 the left side is 3 × 11 = 33 and the right side is 4 × 9 + 7 = 43. They do not match.
The correction is to draw two small arrows from the outside number to each term inside the bracket before you write the expanded line.
Check yourself
Solve each equation and check your answer in the original.
1. 5(x − 2) = 3x + 4
Show answer
Expand: 5x − 10 = 3x + 4. Subtract 3x: 2x − 10 = 4. Add 10: 2x = 14. So x = 7.
Check: 5(7 − 2) = 25 and 3 × 7 + 4 = 25. ✓
2. 2(3x + 1) − (x − 4) = 21
Show answer
Expand, remembering the minus changes both signs: 6x + 2 − x + 4 = 21. Simplify: 5x + 6 = 21. Then 5x = 15, so x = 3.
Check: 2(10) − (3 − 4) = 20 − (−1) = 21. ✓
3. 4(2 − x) = 3(x − 5)
Show answer
Expand: 8 − 4x = 3x − 15. Add 4x to both sides: 8 = 7x − 15. Add 15: 23 = 7x. So x = 23/7.
Check: 4(2 − 23/7) = 4 × (−9/7) = −36/7, and 3(23/7 − 5) = 3 × (−12/7) = −36/7. ✓
Where this leads next
Once brackets feel routine, move on to equations containing fractions, then test everything in the equations and formulas practice set. The non-calculator working trainer helps when the answer is an awkward fraction like 23/7.
Some students follow every line in class but still drop a sign when they work alone. That pattern is exactly what our teachers look for in online one-to-one Mathematics tuition.