These are a bit like equations….but with one really big exception!

The Symbols

> Means greater than
< Means less than
<≥ Means greater than or equal to
<≤ Means less than or equal to

Algebra Inequalities

These are exactly the same as normal equations except:

WHEN YOU MULTIPLY OR DIVIDE BY A NEGATIVE NUMBER YOU FLIP THE INEQUALITY SIGN

Example: 6 – 3x ≤ 9 + x

Minus x and minus 6 from both sides

-4x ≤ 3

Divide by -4 so you flip the sign

x ≥ – 3/4

NOTE: If asked to draw inequalities on a number line use an open circle for > and < and a coloured in circle for ≥ and ≤ then draw a straight line between the values…this is a throwback to KS3.

Graphing Inequalities

You might be asked to show inequalities on a graph. In such a case:

  • Make the inequality into an equation by having x on one side and y on the other
  • Plot 3 points on the graph (you can get away with 2, but 3 is safer)
  • Draw a line between them – make it dotted for < and >, but make it solid for ≤ and ≥
  • Shade the correct side of the line
Example:
inequalities graph
In an exam they will probably give you three inequalities and ask you to shade the area that satisfies all three – usually this is just the triangle in the middle of the three lines.