Chapter 3 Reference Sheet: Solving Inequalities
Inequality
Less than
Symbol

Graph
open circle
Greater than

open circle
Less than or equal to

closed circle
At most
No more than
Greater than or equal to

closed circle
Example
At least
No less than
**As long as the variable is on the left you shade the way the inequality is pointing.
LESS THAN
GREATER THAN
**Always rewrite the inequality if the variable is not on the left.
Example:  2  x , read “x” first states “x less than or equal to -2” so rewrite as x  2
Important Notes:
A solution of an inequality is any number that makes the inequality true.
When solving inequalities, if you multiply or divide by a negative you must flip the inequality symbol.
Example:
-5x > -10
-5
-5
 4  3
 4 
x  3



  3 4
  3
x  4
x<2
**Here is why it works…
 Multiplying or dividing by a negative number changes the meaning of the inequality, see below.
3 > 1, now if I multiply both sides by -2 I now have…
(-2) 3 > 1 (-2)
-6 > - 2, however, this is incorrect -6 is actually less than -2, not greater than!
-6 < - 2, so we need to flip the sign to make the inequality true.
-6
-2 0