Question 1202784
Solve for x

| 2(x+1) + 4 | < 10
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Below I present the solution in very compact form.



<pre>
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  <U>ANSWER</U>
</pre>

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, &nbsp;look into the lesson

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Inequalities/Solving-absolute-value-inequalities-IK.lesson>Solving absolute value inequalities</A> 

in this site.