# What are common mistakes students make with systems of inequalities?

Oct 19, 2015

Number one is probably forgetting to consider reversing the inequality when multiplying both sides by a value that can be negative.

#### Explanation:

For example:

$\frac{x + 1}{x - 1} < 3$

First step - multiply through by $\left(x - 1\right)$ ?

$x + 1 \textcolor{red}{<} 3 x - 3$

Oops! What if $x < 1$?