0580
Linear Equations and Inequalities
Algebra and Sequences
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
Exam tip
Do one operation per line and apply it to both sides. The schemes award a mark for a correct first step on its own, so a neatly shown rearrangement scores even when the arithmetic afterwards goes wrong. Substituting your answer back into the original equation is the check that catches a sign slip.
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