Solve for $x : | x + 4 | < 12$

[- 16, 7]

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(- 16, 4]

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[- 16, 3)

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(- 16, 8)

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Solution

The correct option is B $(- 16, 8)$
Given, $| x + 4 | < 12$
Case 1: When $(x + 4) > 0 \Rightarrow | x + 4 | = x + 4$
Then, $x + 4 < 12 \Rightarrow x < 8$ --- (1)
Case 2: When $(x + 4) < 0 \Rightarrow | x + 4 | = - (x + 4)$
Then, $- x - 4 < 12 \Rightarrow - x < 16 \Rightarrow x < - 16$ --- (2)
From case 1 and 2, we get the solution of $x$ as $(- 16, 8)$

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