Solving Rational Inequalities

Since you cannot cross multiply, the only option to finish an inequality when there are variables on both sides is by getting common denominators.

Example

$\frac{2}{x-5}<-10$ $\frac{2}{x-5}-10<0$ $\frac{2-10(x-5)}{x-5}<0$ $\frac{2-10x+50}{x-5}<0$ $\frac{-10x+52}{x-5}<0$ Get the Critical Values(When numerator is 0, when denominator is 0) Critical values are: x=5, x = 26/5 Then make your Chart Making 6 Columns

test	x < 5	x = 5	5 < x < 26/5	x = 26/5	26/5 < x
(-10x + 52)/(x-5)	-	0	+	0	-