This module covers how to solve linear equations with brackets and fractions, rearrange a formula when the letter you want appears more than once, turn a sentence into an equation, and prove your answer is right by checking it. These skills run through algebra, geometry, graphs and problem-solving questions across the whole course.
Check the current Cambridge IGCSE Mathematics 0580 syllabus for the exact wording of each content point in your exam year. The habits taught here stay the same across versions. Our Mathematics learning guide shows where this module sits among the others.
What should you already know?
You need to expand and collect terms, which is covered in algebraic structure, and to handle negative numbers and fractions confidently. If 3(x − 2) still turns into 3x − 2 in your head, revisit expanding before starting here.
An orienting example
Solve 3(x − 2) = (x + 6)/2 + 4.
Step 1, clear the fraction: multiply every term by 2. That gives 6(x − 2) = (x + 6) + 8.
Step 2, expand: 6x − 12 = x + 14.
Step 3, collect: 6x − x = 14 + 12, so 5x = 26.
Step 4, divide: x = 26/5 = 5.2.
Check in the original: left side 3(5.2 − 2) = 3 × 3.2 = 9.6. Right side (5.2 + 6)/2 + 4 = 5.6 + 4 = 9.6. Both sides match.
That single question used brackets, a fraction and a final check. The five lessons below teach each of those moves on its own first.
In which order should you study it?
- Solve a linear equation with brackets: expanding and balancing, the base for everything else.
- Solve an equation containing fractions: clear denominators in one step instead of working with fractions throughout.
- Rearrange a formula with the variable on both sides: the same balancing, with letters instead of numbers and a factorising step.
- Form an equation from a verbal constraint: turns a sentence into something you can solve.
- Check a solution in the original relationship: the habit that catches errors before the examiner does.
Then work through the mixed practice set. One lesson a day and the practice set at the weekend is a steady pace.
Which traps catch most students here?
- Expanding only the first term of a bracket, so 3(2x − 5) becomes 6x − 5.
- Multiplying only some terms when clearing a fraction, and leaving the whole-number term untouched.
- Moving a term without changing its sign when it crosses the equals sign.
- Translating “3 more than twice” backwards in a word problem.
- Checking in a rearranged line instead of in the original equation.
Each lesson shows one of these slips in full and then corrects it.
How should you use the practice set?
Attempt each question on paper before opening the answer, and write every line of working. A marker gives credit for method, so a clear line-by-line layout protects marks even when the last step goes wrong. The non-calculator working trainer is handy for checking a fraction step by hand.
When a question goes wrong, use the routing notes at the end of the practice set to return to the right lesson. Retry a fresh question a few days later, and record it in the mistake log and retest queue so it does not get lost.
Next in the syllabus, simultaneous relationships builds on these same equation skills with two unknowns. For teaching beyond self-study, online one-to-one Mathematics tuition means an experienced teacher sees your written working and finds which habit sits behind the error.