SOLUTION: i want to know the solution of the following question...plzzzz help me .. Q) 3/|2x-1|≥ 4 also tell me that what is the difference between these two inequalities? 3/|2x

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Question 598019: i want to know the solution of the following question...plzzzz help me ..
Q) 3/|2x-1|≥ 4
also tell me that what is the difference between these two inequalities?
3/|2x-1|≥4 AND 3/|2x-1|>4
can we solve these two in the same way???
Answer by lwsshak3(11628)   (Show Source): You can put this solution on YOUR website!
i want to know the solution of the following question...plzzzz help me ..
Q) 3/|2x-1|≥ 4
also tell me that what is the difference between these two inequalities?
3/|2x-1|≥4 AND 3/|2x-1|>4
can we solve these two in the same way???
**
3/|2x-1|≥ 4
We must solve for 2 conditions because we do not know if the expression within the absolute signs is > 0 or <0.
For (2x-1)>0
3/(2x-1)≥4
3≥8x-4
7≥8x
8x≤7
x≤7/8
..
For (2x-1)<0
3/(-2x+1)≥4
3≥-8x+4
-1≥-8x
divide by -1 and reverse inequality sign
1≤8x
8x≥1
x≥1/8
..
number line:
<........[1/8<===>7/8].............>
solution: [1/8,7/8]
..
To answer your questions:
As you can see from the solution, both inequalities can be solved in the same way.
The important difference is in the solution interval which shows whether or not the end values like 7/8 and 1/8 are included in the interval. ≤ or ≥ means they are included as the brackets [ ] indicate. If only < or > were used, parenthesis ( ) instead would be used. Hope this helps
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