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

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)