Question

Solve the following inequality algebraically. 5 |x + 4| – 4 => 36

Answer 1

To solve the inequality we have to remember the property:

$\lvert x\rvert\ge a\Leftrightarrow x\ge a\lor x\leq-a$

Then:

$\begin{gathered} 5\lvert x+4\rvert-4\ge36 \\ 5\lvert x+4\rvert\ge40 \\ \lvert x+4\rvert\ge\frac{40}{5} \\ x+4\ge8\lor x+4\leq-8 \\ x\ge8-4\lor x\leq-8-4 \\ x\ge4\lor x\leq-12 \end{gathered}$

Therefore the solution is:

$(-\infty,-12\rbrack\cup\lbrack4,\infty)$