Solve the inequality 2- 5*l 2x-3 l < 7

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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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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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