Linear Inequalities (Cambridge International AS Mathematics)

Linear inequalities

What are linear inequalities?

• Similar to equations but answers take a range of values

• Linear means there will be no terms other than degree 1

  • no squared terms or higher powers, no fractional or negative powers

• Number line diagrams are often used

What is interval notation?

• Use of square [] and round () brackets

• [ or ] mean included

• ( or ) mean excluded

  • (4,8] means 4 < x < 8

• Note ∞ always uses ( or )

How do I solve linear inequalities?

• treat as equations but

  • avoid multiplying or dividing by a negative
  • if unavoidable, “flip” the inequality sign so < → >, ≥ → ≤, etc
  • do rearrange to make the x term positive

Worked Example