1 Answer

Ncw · Answer 1 · 2021-11-09T04:06:52+0000

Answer:

$x \geqslant 4 \: or \: x \leqslant - 12$

Explanation:

The given absolute value inequality is:

$5 - |x + 4| \leqslant - 3$

Let us subtract 5 from both sides to get:

$- |x + 4| \leqslant - 3 - 5$

We simplify to get:

$- |x + 4| \leqslant - 8$

We divide through by -1 to get:

$|x + 4| \geqslant 8$

By the definition of absolute value function,

$(x + 4) \geqslant 8 \: or \: - (x + 4) \geqslant 8$

Divide through the second inequality by -1 and reverse the inequality sign.

$(x + 4) \geqslant 8 \: or \: (x + 4) \leqslant - 8$

Subtract 4 from both sides of both inequalities.

$x \geqslant 8 - 4 \: or \: x \leqslant - 8 - 4$

$x \geqslant 4 \: or \: x \leqslant - 12$

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