Question

$solve \: for \: x \: \: \: |x + 4| < 12$



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Answer 1

Step-by-step explanation:

The given inequality is as:

|x + 4| < 12

Separate the inequality into 2 possible cases, that is,

(i) x + 4 < 12, x + 4 _> 0

(ii) -(x + 4) < 12, x + 4 < 0

These can further be written as:

(i) x < 8, x _> - 4

(ii) x > - 16, x < - 4

Now, find the intersection.

(i) x "belongs to" [- 4, 8》

(ii) x "belongs to" 《- 16, - 4》

Find the union i.e.,

x "belongs to" 《- 16, 8》