### Home > INT1 > Chapter 11 > Lesson 11.2.5 > Problem11-110

11-110.

Solve the equations and inequalities below, if possible.

1. $6 |x|> 18$

$x < −3 \text{ or } x > 3$

1. $| 3 x - 2 |≤ 2$

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

$\left|3x-2\right|=2$

Since$\left|±2\right| = 2$, this can be rewritten as two equations. Solve the two equations for $x$ and plot the boundary points on a number line.
$3x − 2 = 2 \quad \quad 3x − 2 = −2$

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

1. $(4x − 2)^2 = 100$

$4x − 2 = 10 \quad \quad 4x − 2 = −10$

1. $(x−1)^3=8$

Look inside. The cube root of $8$ is $2$.