Solve the inequality 2- 5*l 2x-3 l < 7
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calendarEducator since 2008
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2- 5*l 2x-3 l < 7
First we will need to isolate the absolute values on the left side.
Let us subtract 2 from both sides.
==> -5*l2x-3l < 5
Now we will divide by -5 and reverse the inequality.
==> l 2x-3 l > -1
==> 2x-3 > -1
==> 2x > 2
=> x > 1...............(1)
-(2x-3) > -1
==> 2x-3 < 1
==> 2x < 4
==> x < 2...............(2)
Now we will rewrite:
==> -1 < 2x-3 < 1
Add 3 to all sides.
==> 2 < 2x < 4
Now we will divide by 2.
==> 1 < x < 2
Then the values of x belongs to the interval (1, 2)
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calendarEducator since 2010
write12,544 answers
starTop subjects are Math, Science, and Business
The given inequality is 2- 5*l 2x-3 l < 7
2- 5*l 2x-3 l < 7
=> -5*| 2x - 3| < 7 - 2
=> -5*| 2x - 3| < 5
=> | 2x - 3| > -1
This can be written as
2x - 3 > -1 and - ( 2x - 3) > -1
=> 2x > 2 and -2x > -4
=> x > 1 and 2x < 4
=> x > 1 and x < 2
The values of x lie between 1 and 2
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