# How do you solve -4x-8<=56?

Aug 10, 2016

$- 4 x - 8 \le 56$
or
$4 x + 8 \ge - 56$
or
$4 \left(x + 2\right) \ge - 56$
or
$x + 2 \ge - \frac{56}{4}$
or
$x + 2 \ge - 14$
or
$x \ge - 14 - 2$
or
$x \ge - 16$

Aug 10, 2016

$x \ge - 16$

#### Explanation:

Treat an inequality in the same way as an equation, unless you multiply or divide by a negative number, in which case the inequality sign must change around.

We can tackle this question in 2 ways: Compare them.

Make the x-term positive$\textcolor{w h i t e}{\ldots \ldots \ldots \ldots \ldots \ldots \ldots . .}$keep the x-term on left

$- 4 x - 8 \le 56 \textcolor{w h i t e}{\ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots . .} - 4 x - 8 \le 56$

$- 8 - 56 \le 4 x \textcolor{w h i t e}{\ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots . .} - 4 x \le 56 + 8$

$- 64 \le 4 x \text{ "div 4color(white)(....................................)-4x <=64}$

$- 16 \le x \textcolor{w h i t e}{\ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots . .} \frac{- 4 x}{- 4} \textcolor{red}{\ge} \frac{64}{- 4}$

$x \ge - 16 \textcolor{w h i t e}{\ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots .} x \ge - 16$