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

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Answer 1 · 2014-09-10T14:23:04

$- 12 < - 2 (x + 1) \leq 18$ $-12<-2(x+1)<=18$

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

$6 > x + 1 \geq - 9$ $6>x+1>=-9$

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

$5 > x \geq - 10$ $5 > x >= -10$

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 number line

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

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