We discuss inequalities.

Devyn asked what score was needed on the third exam to have an average of 82. This gave us the equation . The solutions only tell us what will give an average exactly 82. It may have been more advantageous to ask what score was needed to have an average of at least 82, yielding not an equation, but an inequality, .

As with equations, there are various types of inequalities.

A linear inequality in is an inequality which is equivalent to , , , or . We solve the inequality in much the same manner as with a linear equation. The main differences come from changing the direction of the inequality when multiplying/dividing by a negative quantity and expressing our answers in interval notation.

Nonlinear inequalities are more complicated. To solve them, we will use a tool called a sign chart. The process requires us to move all the nonzero terms of the inequality to one side, and factor.

Find the solution of the inequality
None of the above