# How do you graph and solve  |3 - 2x| ≥ 4?

Mar 19, 2016

x <= -1/4
x >= 7/2

#### Explanation:

Separate solving in 2 parts:
a. $\left(3 - 2 x\right) \ge 4$
$- 2 x > + 1$
$2 x \le - \frac{1}{2}$ --> $x \le - \frac{1}{4}$
b. -(3 - 2x) >= 4
-3 + 2x >= 4
2x >= 7 --> $x \ge \frac{7}{2}$

Solution set: half-closed intervals (-inf, -1/4] and [7/2, +inf)

========= -1/4 -------- 0 ------------------------------ 7/2 ==============

Note. The 2 end points are included in the solution set

Mar 19, 2016

x is outside the closed interval $\left[- \frac{1}{2} , \frac{7}{2}\right]$. The domain is the real line sans $\left[- \frac{1}{2} , \frac{7}{2}\right]$.

#### Explanation:

$| 3 - 2 x | \ge 4$ is the combined equation for the couple
$3 - 2 x \ge 4 \mathmr{and} 2 x - 3 \ge 4$.

From the first in the pair, $x \le - \frac{1}{2}$.
From the second, $x \ge \frac{7}{2}$.