Lesson 3 of 8

Inequalities & The Flip Rule

Inequalities use the signs less-than, greater-than, less-than-or-equal, and greater-than-or-equal instead of an equals sign. You solve them almost exactly like equations, doing the same thing to both sides.

REMEMBER

If you multiply or divide both sides by a NEGATIVE number, flip the inequality sign. Less-than becomes greater-than, and so on. This is the one rule everyone forgets.

  1. 1Solve -2x + 1 less-than 9
  2. 2Subtract 1 from both sides: -2x less-than 8
  3. 3Divide both sides by -2 AND flip the sign: x greater-than -4

Graphing on a number line

  • Use an OPEN circle for less-than or greater-than (the number is not included)
  • Use a CLOSED (filled) circle for less-than-or-equal or greater-than-or-equal (the number is included)
  • Shade toward the numbers that make it true: right for greater-than, left for less-than

ON THE TEST

Open circle means the dot is hollow, the endpoint is not part of the answer. Filled circle means it counts.