Below I present the solution in very compact form.
Your starting inequality is
| 2(x+1) + 4 | < 10.
It is equivalent to this compound inequality (which represents, actually, two inequalities at the same time)
-10 < 2(x+1) + 4 < 10.
Subtract 4 from all three terms (left term, middle term and right term). You will get
-10 - 4 < 2(x+1) < 10 - 4
or, equivalently,
-14 < 2(x+1) < 6.
Now divide all three terms by 2. You will get
-7 < x+1 < 3.
Last step is to subtract 1 from all three terms. You will get
-8 < x < 2, which is your ANSWER
Solved.
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The major lesson to learn from my post is that
you can make these equivalent transformations
SIMULTANEOUSLY with all three terms of a compound inequality.
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To see many other similar and different SOLVED problems on absolute value inequalities, look into the lesson
- Solving absolute value inequalities
in this site.
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