# How do you solve 18<=-2x+8?

Mar 12, 2017

See the entire solution process below:

#### Explanation:

First, subtract $\textcolor{red}{8}$ from each side of the inequality to isolate the $x$ term while keeping the inequality balanced:

$18 - \textcolor{red}{8} \le - 2 x + 8 - \textcolor{red}{8}$

$10 \le - 2 x + 0$

$10 \le - 2 x$

Now, divide each side of the inequality by $\textcolor{b l u e}{- 2}$ to solve for $x$ while keeping the inequality balanced. However, because we are multiplying or dividing an inequality by a negative term we must reverse the inequality:

$\frac{10}{\textcolor{b l u e}{- 2}} \textcolor{red}{\ge} \frac{- 2 x}{\textcolor{b l u e}{- 2}}$

$- 5 \textcolor{red}{\ge} \frac{\textcolor{b l u e}{\cancel{\textcolor{b l a c k}{- 2}}} x}{\cancel{\textcolor{b l u e}{- 2}}}$

$- 5 \textcolor{red}{\ge} x$

To state the solution in terms of $x$ we must reverse or "flip" the inequality:

$x \le - 5$