What are all real x elements of the set A if they have the property | 3x - 4 | =

The property of the elements of the set A is to make the
inequality to hold.

We'll re-write the property, using
absolute value definition:

-6 =< 3x - 4 =<
6

We'll solve the system of
inequalities:

-6 =< 3x - 4 and 3x - 4 =<
6

We'll begin with the
first:

-6 =< 3x -
4

We'll add 4 both sideS:

-6 +
4 =< 3x

-2 =<
3x

x >= -2/3

We'll
solve the next inequality:

3x - 4 =<
6

We'll add 4 both sides:

3x
=< 6 + 4

3x =<
10

x =< 10/3

The common
interval of values that satisfy both inequalities is representing the set
A.

The set A is the opened interval: (-2/3 ;
10/3).