Solve: | 4 x - 5 | < 6

Question

Give your answer as an interval.

Answer 1

|4x-5| < 6

 

With the absolute value the quantity inside the absolute value...

4x-5 is either less than 6, or greater than -6.  This is written as:

 

-6 < 4x-5 < 6  

 

Work both sides of the inequality separately.

Add 5 on all sides

 

-6 + 5 < 4x < 6 + 5

-1 < 4x < 11

 

Divide all sides by 4

 

-1/4 < x < 11/4

 

So our answer is all x larger than -1/4 and less than 11/4.

As an interval this is

 

(-1/4, 11/4)

 

We use the ( rather than a bracket [ to indicate the value is

not actually included in the interval.