Intermediate Algebra, Chapter 2, 2.7, Section 2.7, Problem 50

Solve $|-3 + x| > 8$. Graph the solution set.

The absolute value inequality is rewritten as

$-3 + x > 8$ or $-3 + x < -8$,

because $-3 + x$ must represent a number that is more than $8$ units from on either side of the number line.We can solve the compound inequality.


$
\begin{equation}
\begin{aligned}

-3 + x > & 8 && \text{or} &&& -3 + x < & -8
&&
\\
x > & 11 && \text{or} &&& x < & -5
&& \text{Add } 3

\end{aligned}
\end{equation}
$



The solution set is $(- \infty, -5) \cup (11, \infty)$.