Yup. Removing the absolute-value symbols in these types of inequalities results in two new inequalities (and, in one case, the two can be written as a single compound inequality).
Here's the rules.
CASE 1
|expression| < value
We can remove the absolute-value symbols by writing:
-value < expression < value
(This is a single compound inequality.)
CASE 2
|expression| > value
We can remove the absolute-value symbols by writing:
expression > value
or
expression < -value
CASE 1 EG
|x + 7| < 15
-15 < x + 7 < 15
Subtract 7 from all three parts, to solve.
-22 < x < 8
CASE 2 EG
|x + 7| > 15
x + 7 > 15
or
x + 7 < -15
Again, subtract 7 from both sides of each to solve.
(-infinity, -22) U (8, infinity)
BtW: Changing FROM less than TO less than or equal (or FROM greater than TO greater than or equal) does not affect these rules.
