0580

Linear Equations and Inequalities

Algebra and Sequences

Reading the symbols

  • An inequality states that one quantity is greater or less than another rather than equal to it
  • < and > are strict, excluding the end value; ⩽ and ⩾ are inclusive
    • x > 5 excludes 5, whereas x ⩾ 5 includes it

Listing integer solutions

  • Test the two ends independently, since one may be included while the other is not
    • For −2 < x ⩽ 3 the integers are −1, 0, 1, 2 and 3
  • The strict end is excluded and the inclusive end is kept
Worked example

Listing the integers that satisfy an inequality

List the integers n for which −2 ⩽ n < 3.

Solution:

  • Read each end symbol separately, because they are not the same
  • ⩽ on the left means −2 is included
  • < on the right means 3 is not included
  • Working up from −2: −2, −1, 0, 1, 2
  • The next integer would be 3, which the strict sign excludes
  • The integers are −2, −1, 0, 1, 2
  • Zero is an integer and is easy to leave out by accident