Solve and graph the absolute value inequality: |2x + 4| > 14.

Solution:

Given function is |2x + 4| > 14

In case of modulus, we rewrite it as 2x + 4 < -14 or 2x + 4 >14

Consider 2x + 4 < -14

Add -4 on both sides

2x +  4 - 4 < -14 - 4

2x < -18

Divide by 2 on both sides

x < -18/2

x < -9

Consider 2x + 4 >14

Add -4 on both sides

2x + 4 - 4 > 14 - 4

2x > 10

x > 10/2

x > 5

graph of the absolute value inequality: |2x + 4| > 14

Therefore, the graph is valid only between x < -9 and x > 5.

Solve and graph the absolute value inequality: |2x + 4| > 14.

Summary:

The absolute value inequality: |2x + 4| > 14 is x < -9 and x > 5.

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