6.5 Solving 6.5 Solving Inequalities by Inequalities by

FactoringFactoring

Steps to SolveSteps to Solve

To solve an inequality by factoring, treat the To solve an inequality by factoring, treat the inequality like an inequality like an sign and solve. sign and solve. Make sure to set the equation Make sure to set the equation to to

first first

These are the solutions to plot on the number These are the solutions to plot on the number line.line.

Use an Use an dot for dot for or or and a and a dot for dot for or or . .

Then, test a point in each region. If it makes the Then, test a point in each region. If it makes the statement statement , shade that region. , shade that region.

Write your solution as an inequality. Write your solution as an inequality.

equalequal zero

open closed

true

< >≤ ≥

Solve each inequality and Solve each inequality and graph the solution set.graph the solution set.

1.1. 2. 2. d2 −9d+14 < 0 y

2 −4y≤5

Solve each inequality and Solve each inequality and graph the solution set.graph the solution set.

3.3. 4. 4. x3 < 9x x

2 −3x>10

Solve each inequality and Solve each inequality and graph the solution set.graph the solution set.

5.5. 6. 6. 5 f 2 −180 > 0 4w3 + 25w> 20w2