### Home > CAAC > Chapter 12 > Lesson 12.1.2 > Problem 12-17

12-17.

Solve the equations and inequalities below. Check your solutions, if possible. Homework Help ✎

| 5

*x*+ 8 | > − 4*x*^{2}+*x*− 20 < 02

*x*^{2}− 6*x*= − 53

*x*(2*x*− 5*y*+ 4)

Set up two equations to remove the absolute value.

5*x* + 8 = −4 or 5*x* + 8 = 4

5*x* = 12 or 5*x* = −4

Test numbers to see which region is the solution.

What does it mean if both regions come out true?

Treat the inequality like an equation and factor.

Use the Zero Product Property to solve for *x* then test numbers to determine which region is the solution.

No solution.

First multiply both sides of the equation by 9 to remove the fractions.