Mathematics (Core)Exam code: 0580
Linear Equations
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