What are all real x elements of the set A if they have the property | 3x - 4 | = < 6 ?

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

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We have to find all the values of x that satisfy | 3x - 4| =< 6

|3x - 4| =< 6 gives us two inequations:

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

=> 3x =< 10 and -3x =< 2

=> x =< 10/3 and x => -2/3

The required set A is ( -2/3 , 10/3)

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giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

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).

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