# Find the values of x that satisfy the inequality |(3x + 1)/2| < 1.

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We have the inequality | (3x + 1)/2| < 1 to solve for x.

Now as the absolute value of (3x+1)/2 is less than 1, we can convert the inequality to the following form: -1 < (3x+1)/2 < 1.

multiplying all terms by 2

=> -2 < (3x+1) < 2

subtract 1 from all the terms

=> -3 < 3x < 1

divide all the terms by 3

=> -1 < x < 1/3

Therefore x lies in the range -1 < x < 1/3.

**The required values of x are -1 < x < 1/3.**

We'll write the conditions:

-1<(3x + 1)/2 < 1

We'll solve the simultaneous inequalities:

-1<(3x + 1)/2

-2<3x + 1

-3<3x

We'll divide by 3:

x>-1

We'll solve the other inequality:

(3x + 1)/2 < 1

3x + 1 < 2

We'll subtract 1 both sides:

3x < 1

We'll divide by 3:

x < 1/3

**So, the interval of x values for the expression |(3x + 1)/2| < 1 is true is: (-1 ; 1/3).**