# How do you solve −5x + 8 <= x − 4?

Aug 15, 2015

$x \ge 2$

#### Explanation:

Isolate $x$ on one side of the inequality, first by adding $- x$ to both sides to get

$- 5 x + 8 - x \le \textcolor{red}{\cancel{\textcolor{b l a c k}{x}}} - \textcolor{red}{\cancel{\textcolor{b l a c k}{x}}} - 4$

$- 6 x + 8 \le - 4$

Next, add $- 8$ to both sides of the inequality

$- 6 x + \textcolor{red}{\cancel{\textcolor{b l a c k}{8}}} - \textcolor{red}{\cancel{\textcolor{b l a c k}{8}}} \le - 4 - 8$

$- 6 x \le - 12$

FInally, divide both sides by $- 6$, but do not forget that you need to change the sign of the inequality when you're multiplying or dividing by a negative number

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{- 6}}} x}{\textcolor{red}{\cancel{\textcolor{b l a c k}{- 6}}}} \textcolor{red}{\ge} \frac{\left(- 12\right)}{\left(- 6\right)}$

$x \ge \textcolor{g r e e n}{2}$

So, for any value of $x$ that is greater to or equal than $2$, your original inequality will be true.