1. Solving Inequalities

2. Remember a < b means a is less than b
a ≤ b means a is less than or equal to b
a > b means a is greater than b
a ≥ b means a is greater than or equal to b

3. Solve ≥ 2x - 3 First multiply each side by 3 x ≥ 6x – 9
Add 9 to each side
x + 9 ≥ 6x
Subtract x from each side
9 ≥ 5x
Divide each side by 5
1.8 ≥ x
Rewrite with x as the subject.
x ≤ 1.8
Note that the inequality sign has changed direction too!
With inequalities you can’t just swap sides!

4. Solve 2( 3x – 1) > 4x + 7 Multiply out the brackets
Add 2 to each side
6x > 4x + 9
Subtract 4x from each side
2x > 9
Divide each side by 2
x > 4½

5. Solve the following 2x + 3 < 5 5x – 4 > 10 – 2x
> 3
2(x + 3) < 1 – 3x
3(2x - 1) ≥ 11 - x