# How do you solve the inequality -5-x/6> -9?

May 23, 2018

See a solution process below:

#### Explanation:

First, add $\textcolor{red}{5}$ to each side of the inequality to isolate the $x$ term while keeping the inequality balanaced:

$- 5 + \textcolor{red}{5} - \frac{x}{6} > - 9 + \textcolor{red}{5}$

$0 - \frac{x}{6} > - 4$

$- \frac{x}{6} > - 4$

Now, multiply each side of the inequality by $\textcolor{b l u e}{- 6}$ to solve for $x$ while keeping the inequality balanced. However, because we are multiplying or dividing an inequality by a negative number we must reverse the inequality operator:

$\textcolor{b l u e}{- 6} \times - \frac{x}{6} \textcolor{red}{<} \textcolor{b l u e}{- 6} \times - 4$

$\frac{\textcolor{b l u e}{6} x}{6} \textcolor{red}{<} 24$

$\frac{\cancel{\textcolor{b l u e}{6}} x}{\textcolor{b l u e}{\cancel{\textcolor{b l a c k}{6}}}} \textcolor{red}{<} 24$

$x < 24$

May 23, 2018

$x < 24$

#### Explanation:

When working with inequalities it is a good idea to work with a positive variable term. This avoids problems with the inequality sign,

$- 5 \textcolor{b l u e}{- \frac{x}{6}} > \textcolor{red}{- 9}$

Move the $\textcolor{b l u e}{- \frac{x}{6}}$ term to the right side and the $\textcolor{red}{- 9}$ to the left.

(Add $\frac{x}{6} \mathmr{and} 9$ to both sides)

-5" "color(red)(+9)" "color(blue)(-x/6 +x/6) > color(red)(-9 +9) ""color(blue)(+x/6)

$\text{ "4 > x/6" } \leftarrow \left(\times 6\right)$

$\text{ } 24 > x$

This is the same as $x < 24$