3 l 2 - 5x l+ 1

To determine all x values, we'll work a bit over the given
expression.

3 l 2 - 5x l+ 1 <
10

We'll subtract 1 both
sides:

3 l 2 - 5x l < 10 -
1

3 l 2 - 5x l <
9

We'll divide by 3:

 l 2 - 5x
l < 9

We'll write the expression as a double
inequality:

-9 < 2 - 5x <
9

We'll solve the left
inequality:

-9 < 2 -
5x

-11 < -5x

We'll use
the symmetric property:

-5x >
-11

We'll multiply by -1:

5x
< 11

We'll divide by
5:

x < 11/5

We'll solve
the right inequality:

 2 - 5x <
9

-5x < 9-2

-5x
< 7

We'll divide by
-5:

x >
-7/5

The admissible values for x belong to
the interval (-7/5 , 11/5).