# How do you solve -10/(x-5)>=-11/(x-6)?

Oct 2, 2016

Get rid of the fractions and divide everything by a negative including the $\ge$ sign.

#### Explanation:

Multiply both sides by (x-5)(x-6) This will get rid of the fractions.

$\left(x - 5\right) \left(x - 6\right) \times - \frac{10}{x - 5} \ge \left(x - 5\right) \left(x - 6\right) \times - \frac{11}{x - 6}$ This gives

$\left(x - 6\right) \times - 10 \ge \left(x - 5\right) \times - 11$ multiplying across the ( ) gives

$- 10 x + 60 \ge - 11 x + 55$ adding + 10x to both sides gives

$- 10 x + 10 x + 60 \ge - 11 x + 10 x + 55$ resulting in

$+ 60 \ge - 1 x + 55$ subtract 55 from both sides

$+ 60 - 55 \ge - 1 x + 55 - 55$ +5 resulting in

$+ 5 \ge - 1 x$ Now divide everything by -1

$+ \frac{5}{-} 1 \frac{\ge}{-} 1 \left(- 1 \frac{x}{-} 1\right)$

$+ \frac{5}{-} 1$ = -5 the opposite of +5

$\frac{\ge}{-} 1$ = $\le$ The opposite of $\ge$

$- 1 \frac{x}{-} 1$ = + 1 x The opposite of -1 x so the answer is

$x \ge - 5$