Question 150360: |-3x-5|>=2
The answer should have form b < x < c
or the form x < b or x > c
Is all my paper says to do.
I dont understand HOW they want me to put it in that form and do the problem.
The topic on the paper says, Absolute Value Inequalities.
I would greatly appreciate it if someone coul dhelp me figur eout how to do this, and show me how they had done it so i can learn how to do it myself.
Thanks,
KKG.: |-3x-5|>=2
The answer should have form b < x < c
or the form x < b or x > c
Is all my paper says to do.
I dont understand HOW they want me to put it in that form and do the problem.
The topic on the paper says, Absolute Value Inequalities.
I would greatly appreciate it if someone coul dhelp me figur eout how to do this, and show me how they had done it so i can learn how to do it myself.
Thanks,
KKG.
Answer by Edwin McCravy(2087)  (Show Source):
You can put this solution on YOUR website!
--------------------------------------------
Learn rules for removing absolute values from
inequalities of these forms:
Rule 1:
-------------------------------------------
 ,  (where N is not negative)
Write as
 ,  , respectively.
then solve. [If N is negative, there is no solution,
and solution set = Ø)
------------------------------------------------------
------------------------------------------------------
Rule 2:
-------------------------------------------
 ,  (where N is not negative)
Write as
   ,  
respectively.
Then solve each part. (If N is negative, solution set is
"all real numbers".)
------------------------------------------
You need Rule 2. I gave you Rule 1 also because you
will need it for other problems:
So write:
 
Solve each part:
Add 5 to both sides of both parts:
 
Divide both sides of both parts by  ,
Notice that dividing an inequality by a NEGATIVE
NUMBER reverses the inequality sign:
 
 
So we shade the number line:
1. to the right of -1
and
2. to the left of  , which is the same as   .
<=======@-----------@==================>
-3 -2 -1 0 1
The circles should be darkened since the inequalities
are all underlined:
Solution in interval notation is
( ,] U [ , )
Edwin
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