You may want to review absolute-value inequalities and solving absolute-value equations first.

Absolute-value inequalities require you to pull together lots of
things you've learned. Suppose you have |*x* − 2|
− 3 ≤ 2, First, you have to get the absolute value by
itself on one side. Now we have |*x* − 2| ≤ 5.

The tricky part is that now we have to solve
the *equation* |*x* − 2| = 5. Its solution is
{7, −3}. But that's just the solution of the equation, not
of the inequality. To solve the inequality, we need to put those
numbers into either an interval or a union of intervals, using the
table here, only backwards. Since our
inequality had a ‘≤’ sign, the answer is [−3,
7]. Note that the smaller number always comes first. With braces,
that doesn't matter, but with intervals it does.

Sometimes (where the inequality has a ‘>’ or ‘≥’), you'll need to write the union of two intervals. That's why I left two spaces for you, with a ‘∪’ between them. If you only need one, just leave the second blank.

Once you've gotten the absolute value by itself, you should
always check that the right-hand side isn't negative. If it's
negative, then it won't match *any* pattern in the table.
In that case, if the inequality has a ‘≤’ or a
‘<’, it's a contradiction. On this website, you can
say so by leaving *both* spots for the answer blank. (Your
teacher might want you to say so some other way.) If the
inequality has a ‘≥’ or a ‘>’, then
it's an identity. Since that means it's right no matter
what *x* is, you can write that as the interval
(−∞, ∞). (If you decide it's a contradiction or
an identity for some other reason, you should also say so the same
way.)