MathematicsExam code: 0580
Linear Equations and Inequalities
Algebra and Sequences
Solving Linear Equations
What makes an equation linear
- A linear equation contains an unknown whose highest power is 1, so there is no x² term
- Solving means isolating the unknown by undoing each operation applied to it
- Whatever is done to one side must be done to the other, which is what keeps the equation true
The method
- Undo additions and subtractions first, then multiplications and divisions
- Work one operation per line so each step is visible
Worked example
A two-step equation
Solve 5x − 8 = 22.
Solution:
- Adding 8 to each side clears the subtraction, leaving 5x = 30
- Since 5 multiplies the unknown, undo it by dividing each side by 5
- x = 6
Exam tip
A correct first line scores on its own
Your first correct move earns a mark on its own: 5x = 30 above keeps that mark even if the division then goes wrong. With a bracket or fractions, the line that collects the unknown on one side earns a second mark, which still counts when it follows correctly from a first line with a slip. Only the last mark needs the right answer, so write every move down rather than jumping to the answer.