Question 1116225
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Since the post by @stanbon contained errors,  I copied,  pasted,  corrected it and presented in more readable format:


 HOW do I do this?: 
Solve each absolute value inequality and show it's solution set:


<pre>
a) |x| <= 3

   -3<= x <=3

====================

b) |3-x| < 5

   -5 < 3-x < 5
   -8 < -x < 2    
   -2 < x < 8    <<<---=== those "x", that are remoted less than 5 units from the point  "3" in the number line.

====================

c) |4g-5| > 17

   4g-5 < -17  or  4g-5 > 17
   g < -3 or g > 11/2           <<<---=== the solution is the union of two sets

====================

d) |4x+1| < 21 

   -21 < 4x+1 < 21
   -22 < 4x < 20
   -11/2 < x < 5
</pre>

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For those who learn the solution of absolute value equations for the first time in their life, &nbsp;there is a group of lessons

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/absolute-value/-Absolute-Value-equations.lesson>Absolute Value equations</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/absolute-value/HOW-TO-solve-equations-containing-Linear-Terms-under-Abs-Value-sign-L-1.lesson>HOW TO solve equations containing Linear Terms under the Absolute Value sign. Lesson 1</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/absolute-value/HOW-TO-solve-equations-containing-Linear-Terms-under-Abs-Value-sign-L-2.lesson>HOW TO solve equations containing Linear Terms under the Absolute Value sign. Lesson 2</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/absolute-value/HOW-TO-solve-equations-containing-Linear-Terms-under-Abs-Value-sign-L-3.lesson>HOW TO solve equations containing Linear Terms under the Absolute Value sign. Lesson 3</A>

in this site.


Read them attentively and become an expert in this area. &nbsp;&nbsp;Start from the very first lesson of the list.



Also, you have this free of charge online textbook in ALGEBRA-I in this site

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson>ALGEBRA-I - YOUR ONLINE TEXTBOOK</A>.


The referred lessons are the part of this online textbook under the topic
"<U>Solving Absolute values equations</U>".



Save the link to this online textbook together with its description


Free of charge online textbook in ALGEBRA-I

https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson


to your archive and use it when it is needed.