# How do you solve -8<=2x-4<6?

Mar 2, 2018

Using both inequalities. See below

#### Explanation:

From $- 8 \le 2 x - 4$ Sum 4 to both sides

$4 - 8 \le 2 x - 4 + 4$

$- 4 \le 2 x$ and then $- 2 \le x$ this is the same that $x \ge - 2$

Now, From $2 x - 4 < 6$ Add 4 to both sides

$2 x - 4 + 4 < 6 + 4$ and then

$2 x < 10$ Which is $x < 5$

Collecting all results, we have $x$ must be $x \ge - 2$ and $x < 5$

This is the interval $\left[- 2 , 5\right)$ The solution is all $x$ belonging to this interval $x \in \left[- 2 , 5\right)$ or using set notation

$\left\{x \in \mathbb{R} / x \ge - 2 \mathmr{and} x < 5\right\}$

Mar 2, 2018

Solution : $- 2 \le x < 5$ In interval notation: $x | \left[- 2 , 5\right)$

#### Explanation:

$- 8 \le 2 x - 4 < 6 \mathmr{and} - 8 + 4 \le 2 x - 4 + 4 < 6 + 4$ or

$- 4 \le 2 x < 10 \mathmr{and} - \frac{4}{2} \le \frac{2 x}{2} < \frac{10}{2}$ or

$- 2 \le x < 5 \therefore$ Solution : $- 2 \le x < 5$

In interval notation: $x | \left[- 2 , 5\right)$ [Ans]