Question 1203651
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4|2x+3|-7 < 9
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<pre>
They want you solve this inequality.


Move -7 to the right with changing the sign.  You will get

    4*|2x+3| < 9 + 7,  or

    4*|2x+3| < 16.


Divide both sides by 4.  You will get

    |2x+3| <4.


It means that

    -4 < 2x+3 < 4.


Move 3 from the central part to the left and to the right, changing the sign.  You will get  

    -4 - 3 < 2x < 4 - 3,

or

    -7 < 2x < 1.


Divide everything by 2.  You will get

    -3.5 < x < 0.5.


It is your <U>ANSWER</U>:  the solution set is  -3.5 < x < 0.5,  or the interval (-3.5,0.5),
which does not include the endpoints.
</pre>

Solved, with complete explanations.


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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.