find x values if l 2x -5 l + 7

To find values of the inequality |2x-5| < 10
.

We know that |x-n| = x-n ix x >n and  |x-n| = n-x if
x< n.

Therefore |2x-5| = 2x-5 for 2x-5 > 0. Or x
> 5/2.

Therefore or x > 5/2 , |2x-5| < 10 
implies 2x-5 < 10

2x-5 < 10 implies 2x-5+5 <
10+5 , as  we added equals to both side.

2x <
15.

2x < 15 implies x < 15/2 = 7.5 , as we divided
 both sides by positive equals.

Therefore x>2.5
, x < 7.5.

When x < 2.5 ,
|2x-5| < 10 implies 5-2x < 10.

We add 2x to both
sides:

5 < 10 +2x.

5-10 <
10+2x-10.

-5 < 2x

-5/2 <
2x/2

-2.5 < x. Or x >
-2.5.

Therefore  x  < -2.5 for any x <
=2.5.

Therefore x  is in the interval
(-2.5 , 7.5} but the strict inequality does allow  x  to take boundary
values.