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

Answer 2

The inequality Amber should graph is:

-31  <  x  <  19

The given inequality is:

|x  +  6| -  12  <  13

This can be simplified as:

|x  +  6|  <  12 +  13
|x  +  6|  <  25

This has two solutions:

x  +  6  <  25

x  <  25 - 6

x  <  19

Also:

x  + 6 > -25

x    > -25 - 6

x  > -31

Therefore, the inequality that Amber will graph is:

-31  <  x  <  19

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