Question

Select all the correct answers. Which two inequalities can be used to find the solution to this absolute value inequality? 3|x + 4| − 5 < 7 x + 4 < 4 -3(x + 4) > 12 3(x + 4) < -12 x + 4 < 7 x + 4 > -4 x + 4 > -7

Answer 1

The absolute value inequality can be decomposed into two simpler ones.

x < 0

x > -8

Which two inequalities can be used?

Here we start with the inequality:

3|x + 4| - 5 < 7

First we need to isolate the absolute value part:

3|x + 4| < 7 + 5

|x + 4| < (7 + 5)/3

|x + 4| < 12/3

|x + 4| < 4

The absolute value inequality can now be decomposed into two simpler ones:

x + 4 < 4

x + 4 > - 4

Solving both of these we get:

x < 4 - 4

x > -4 - 4

x < 0

x > -8

These are the two inequalities.

Learn more about inequalities:

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