solve for x if l 2x -3 l

To solve the inequality l 2x -3 l < 5, we'll apply
the rule of the absolute values:

-5 < 2x-3 <
5

Now, we'll solve the left side of the double
inequality:

-5 <
2x-3

We'll isolate 2x to the right
side:

-5+3 < 2x

-2
< 2x

We'll divide by
2:

-2/2 <
x

-1 <
x

We'll solve the right side of the
equation:

2x-3 <
5

We'll isolate to the left side,
2x:

2x < 5+3

2x
< 8

We'll divide by 2 and since is not a negative
value, the inequality remains the same:

x
< 4

So, the interval of x values for
the inequality to hold is:

(-1 ,
4)