# What is variable x if |3x-5|<8?

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We are asked to find the value of x when we are given that the absolute value of the expression (3x -5) is less than 8.

Since we are dealing with absolute value, there are two cases to consider which can be expressed as follows:

=> -8 < 3x-5 < 8

We solve this inequality as follows:

=> -8 < 3x -5 < 8

=> -8 + 5 < 3x -5 + 5 < 8 + 5

=> -3 < 3x < 13

=> -1 < x < 13/3

** The answer is -1 < x < 13/3.**

We have to solve |3x-5|<8 for x.

|3x-5|<8 gives us

3x - 5 < 8 and -8 < 3x - 5

- 3x - 5 < 8

=> 3x < 13

=> x < 13/3 ...(1)

- -8 < 3x - 5

=> -3 < 3x

=> -1 < x ...(2)

From (1) and (2) we get that x lies in (-1 , 13/3).

**The solution of the inequality are all values if x that lie in (-1 , 13/3)**

We'll apply the absolute value property, such as:

-8 < 3x - 5 < 8

We'll solve the left side inequality:

-8 < 3x - 5

We'll isolate 3x to the right side:

-8 + 5 < 3x

-3 < 3x

We'll divide by 3:

x > -1

We'll solve the right side inequality:

3x - 5 < 8

We'll isolate 3x to the left side:

3x < 8 + 5

3x < 13

x < 13/3

-1 < x < 13/3

**The values of x that make the inequality to hold are located in the range (-1 , 13/3).**