Answer
$(-\infty,-3)\cup (7,\infty)$
Work Step by Step
We are asked to solve the absolute value inequality:
$|x-2|\gt 5$
We remove the absolute value sign by splitting the inequality into two as follows:
$x-2 \lt -5$ or $x-2 \gt 5$
Now, we solve for (isolate) $x$:
$x-2+2 \lt -5+2$ or $x-2+2 \gt 5+2$
$x \lt -3$ or $x \gt 7$
In interval notation, this can be written as:
$(-\infty,-3)\cup (7,\infty)$
See the number line graph below.
