# How do you solve -4/5(x-3)≤-12?

Jun 15, 2016

$x \ge 18$

#### Explanation:

Treat inequalities in exactly the same way as an equation unless you are are multiplying or dividing by a negative number. In this case the inequality sign has to change around.
Also do not cross-multiply across an inequality.

Let's get rid of the annoying fraction outside the bracket by multiplying by $\frac{5}{4}$, leaving the minus sign there for now.

$\textcolor{red}{\frac{5}{4}} \times - \frac{4}{5} \left(x - 3\right) \le \textcolor{red}{\frac{5}{4}} \times - 12$

$= - \left(x - 3\right) \le - 15 \text{ Multiplying out gives}$

$\text{ } = - x + 3 \le - 15$

The problem now is the $- x$. The easiest is to move it to the right side to make it positive ;

$15 + 3 \le x$

$18 \le x$ which can also be written as $x \ge 18$

The other method would involve dividing by -1.
$- x \le - 15 - 3$
$- x \le - 18 \text{ divide by -1 "rArr" sign will change}$

$x \ge 18$