What is the answer and how do you solve and graph on a number line this equation??

Question

What is the answer and how do you solve and graph this absolute value inequality? I will use "l" for the absolute value symbols. -4lx+3l > -20
Thank you!

Answer 1

First isolate the absolute value. Divide both sides by -4. Multiplying or dividing and inequality by a negative reverses the order.

 

-4 |x + 3| ≥ -20

|x + 3| ≤ 5

 

Absolute values are solved twice. Once assuming the number (here x + 5) is positive and then assuming it is negative.

 

I. |x + 3| ≤ 5               positive

    x + 3 ≤ 5

    x ≤ 3

 

II. |x + 3| ≤ 5             negative

     -(x + 3) ≤ 5

     -x - 3 ≤ 5

     -x ≤ 8

     x ≥ -8                    multiplied by a negative, order changes

 

Closed dot on -8 line extending to closed dot on 3.