# How do you solve (-x+8)/(x-2)>=5?

Dec 24, 2016

$x \le 3$

#### Explanation:

If we start with $\frac{- x + 8}{x - 2} \ge 5$, then our first step should be to get rid of the denominator. To do that, we multiply both sides by $\left(x - 2\right)$. That changes the eqaution into $\frac{- x + 8}{\cancel{x - 2}} \ge 5 \cdot \left(x - 2\right)$. If we distribute the $5$, it becomes $- x + 8 \ge 5 x - 10$. Just add $x$ and $10$ on both sides, and we are left with $18 \ge 6 x$. Divide by $6$ on each side, and we see that $3 \ge x$. The conventional way to write inequalities is to have the variable first, so we shouls rewrite it as $x \le 3$