### Home > CC4 > Chapter 11 > Lesson 11.2.5 > Problem 11-110

11-110.

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

a.

6

> 18 b.

≤ 2 c.

(4

*x*− 2)^{2}= 100d.

(

*x*− 1)^{3}= 8

*x* < −3 or *x* > 3

Begin by changing the inequality to an equation and solve for the boundary points.

Since |±2| = 2, this can be rewritten as two equations. Solve the two equations for *x* and plot the boundary points on a number line.

3*x* − 2 = 2 3*x* − 2 = −2

Test points on the number line in the original inequality to find the regions that make it true. Shade them and describe them algebraically.

4*x* − 2 = 10 4*x* − 2 = −10

Look inside. The cube root of 8 is 2.