Question

Amber is solving the inequality |X+6|- 12 <13 by graphing. Which equations should Amber graph?

Answer 1

Answer:

We start at:

|X+6|- 12 < 13

Here we can add 12 to both sides:

|X+6| <13 + 12 = 25

|X+6| < 25

We can separate it in two equations:

if x > -6, then |X+6|  = x + 6

        (x + 6) < 25

         x < 25 - 6

          x <  19

if x < -6, then |X+6|  = -(x + 6)

         -(x + 6) < 25

          -x < 31

            x > -31

And with those two equations we get:

-31 < x < 19