# How do you solve -2( x - 4) \leq 3x?

Feb 21, 2017

$x \ge \frac{8}{5}$

#### Explanation:

$- 2 \left(x - 4\right) \le 3 x$

Expand the parenthesis
$- 2 x + 8 \le 3 x$

add $2 x$ both side.
$2 x - 2 x + 8 \le 3 x + 2 x$
$8 \le 5 x$

divide 5 to both side
$\frac{8}{5} \le \frac{5 x}{5}$

$\frac{8}{5} \le x$ or $x \ge \frac{8}{5}$

Feb 21, 2017

See the entire solution process below:

#### Explanation:

First, expand the terms within parenthesis:

$\left(\textcolor{red}{- 2} \times x\right) - \left(\textcolor{red}{- 2} \times 4\right) \le 3 x$

$- 2 x + 8 \le 3 x$

Next, add $\textcolor{red}{2 x}$ to each side of the inequality to isolate the $x$ term while keeping the inequality balanced:

$\textcolor{red}{2 x} - 2 x + 8 \le \textcolor{red}{2 x} + 3 x$

$0 + 8 \le \left(2 + 3\right) x$

$8 \le 5 x$

Now, divide each side of the inequality by $\textcolor{red}{5}$ to solve for $x$ while keeping the inequality balanced:

$\frac{8}{\textcolor{red}{5}} \le \frac{5 x}{\textcolor{red}{5}}$

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

$\frac{8}{5} \le x$

To put the solution in terms of $x$ we can reverse or "flip" the inequality:

$x \ge \frac{8}{5}$