# How do you solve -8x>24?

Feb 25, 2017

See the entire solution process below:

#### Explanation:

Divide each side of the inequality by $\textcolor{b l u e}{- 8}$ to solve for $x$ while keeping the inequality balanced. However, because we are multiplying or dividing by a negative term we must reverse the inequality:

$\frac{- 8 x}{\textcolor{b l u e}{- 8}} \textcolor{red}{<} \frac{24}{\textcolor{b l u e}{- 8}}$

$\frac{\textcolor{b l u e}{\cancel{\textcolor{b l a c k}{- 8}}} x}{\cancel{\textcolor{b l u e}{- 8}}} \textcolor{red}{<} - 3$

$x < - 3$

Feb 25, 2017

Just a slightly different approach plus demonstrating a very important fact about reversal of the inequality.

$x < - 3$

#### Explanation:

Given:$\text{ } - 8 x > 24$

We wish to have the $x$ value as positive so multiply both sides by $\left(- 1\right)$

There is a trap in doing this: Multiply by negative 1 and you reverse the inequality.

Doing it incorrectly $\to 8 x > - 24 \textcolor{red}{\leftarrow \text{ this is very wrong}}$
Doing it correctly $\textcolor{w h i t e}{.} \to 8 x < - 24 \textcolor{g r e e n}{\leftarrow \text{ correct way round}}$

Divide both sides by 8

$\frac{8}{8} x < - \frac{24}{8}$

But $\text{ "8/8=1" and } 24 \div 8 = 3$

$\text{ } x < - 3$