Symbols
● < → less than
● > → greater than
● ≤ → less than or equal to
● ≥ → greater than or equal to
● Number line inequalities – filled-in circle means ‘or equal to’
● Graphical inequalities – solid line means ‘or equal to’
Linear Inequalities
● Involves only x terms and constants
● Solve linear inequalities as you would solve an algebraic equation for the
most part
● However if you multiply or divide each side by a negative number the
inequality symbol must be reversed
● Check solutions by picking a number and plugging it into the inequality to
see if it satisfies your solution
Example
Solve 1 – x ≥ 2x – 5
1 – x ≥ 2x – 5
1 ≥ 3x – 5
6 ≥ 3x
x ≤ 2
Quadratic Inequalities
● Quadratic inequalities solved by factorising quadratic expression
● The numbers in the brackets tell you the boundaries of the solutions
● To decide which inequality signs to use, visualise graph
Example
Solve 3 – 5x ≤ 2x2
3 – 5x – 2x2 ≤ 0
2x2 + 5x – 3 ≥ 0
(2x – 1)(x + 3) ≥ 0
x ≥ 1/2 or x ≤ – 3
