Three times a number increased by one is between negative eight and seven find all the numbers. All the numbers that makes the statement true are given by?

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This is about absolute value inequalities.

The set of possible values of x that make the statement true are; x = {-2, -1, 0, 1}

We are told that when it is multiplied by 3 and 1 added to it, it is between - 8 and 7. This means it is greater than -8 but less than 7.

Thus;

3x + 1 > -8  - - - (eq 1)

3x + 1 < 7  - - - (eq 2)

3x + 1 > -8

Subtract 1 from both sides to get;

3x > -9

x > -9/3

x > -3

3x + 1 < 7

Subtract 1 from both sides to get;

3x < 7 - 1

3x < 6

x < 6/3

x < 2

Thus, we can write that;

-3 < x < 2

Thus, the set of possible values of x are; x = {-2, -1, 0, 1}

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