Question

|13x-4|+12 < 56
Anybody know this cuz I do

Answer 1

`\displaystyle x\in \left(-(40)/(13),(48)/(13)\right)`

Explanation:

Inequalities with Absolute Value

We must recall the following rule:

`\text{If }|M|<N,\ N>0`

Then:

`-N<M<N`

We have the following inequality:

`|13x-4|+12 < 56`

Subtracting 12:

`|13x-4|< 56-12`

`|13x-4|< 44`

Applying the rule:

`-44<13x-4<44`

Adding 4:

`-44+4<13x<44+4`

Operating:

`-40<13x<48`

Dividing by 13:

`\displaystyle -(40)/(13)<x<(48)/(13)`

The solution expressed in interval form is:

`\boxed{\displaystyle x\in \left(-(40)/(13),(48)/(13)\right)}`