# How do I solve the polynomial inequality -12<-2(x+1)<=18?

Sep 10, 2014

$- 12 < - 2 \left(x + 1\right) \le 18$

Step 1: Divide all three "parts" by -2 and switch the direction of the inequality symbols.

$6 > x + 1 \ge - 9$

Step 2: subtract 1 from all three "parts".

$5 > x \ge - 10$

For your solution, you may need to draw a number line. Be sure to use an open circle at 5 and a closed circle at -10.

My students are also required to use interval notation: $\left[- 10 , 5\right)$