• \( x < y \) means \( x \) is less than \( y \).
  • \( x > y \) means \( x \) is greater than \( y \).
  • \( x \le y \) means \( x \) is less than or equal to \( y \).
  • \( x \ge y \) means \( x \) is greater than or equal to \( y \).

When representing inequalities on a number line, \( \circ \) is used for \( < \) or \( > \); \( \bullet \) is used for \( \le \) or \( \ge \).

Inequalities can be solved in a very similar way to linear equations:

  • you can add or subtract any number on both sides of the inequality.
  • you can multiply or divide by a positive number on both sides of the inequality.

HOWEVER, when you multiply or divide by a negative number you must swap the sign around:
that is, \( < \) becomes \( > \) and vice versa; \( \le \) becomes \( \ge \) and vice versa.

Example videos

Video: https://www.youtube.com/embed/hG_fW-AQ9xQ

Video: https://www.youtube.com/embed/hG_fW-AQ9xQ

Practice questions

Solving linear inequalities - questionsSolving linear inequalities - worked solutions