# How do you solve the x in -ax+2b>8?

Jan 2, 2017

See full solution process details below:

#### Explanation:

The first step is to subtract $\textcolor{b l u e}{2 b}$ from each side of the inequality to isolate the $x$ term:

$- a x + 2 b - \textcolor{b l u e}{2 b} > 8 - \textcolor{b l u e}{2 b}$

$- a x + 0 > 8 - \textcolor{b l u e}{2 b}$

$- a x > 8 - \textcolor{b l u e}{2 b}$

Now we can divide each side of the inequality by $\textcolor{red}{- a}$ to solve for $x$ and keep the inequality balanced.

However, because we are multiplying or dividing by a negative term we need to also reverse the inequality:

$\frac{- a x}{\textcolor{red}{- a}} \textcolor{g r e e n}{<} \frac{8 - \textcolor{b l u e}{2 b}}{\textcolor{red}{- a}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{- a}}} x}{\cancel{\textcolor{red}{- a}}} \textcolor{g r e e n}{<} \frac{8 - \textcolor{b l u e}{2 b}}{\textcolor{red}{- a}}$

$x < \frac{8 - 2 b}{-} a$