Question

Solve the absolute value inequality: [X + 12[ +5 <27

Isolate the absolute value by subtracting 5 from both sides.
18+71<27
18+71<22
|x + 12[ < 22
|x + 121 > 22

Answer 1

Option C.

Explanation:

The given absolute value inequality is

`|x+12|+5<27`

Isolate the absolute value by subtracting 5 from both sides.

`|x+12|+5-5<27-5`

`|x+12|+0<22`

`|x+12|<22`

Therefore, the correct option is C.

We can further solve this, to find the solution of the given inequality.

`-22<x+12<22`

Subtract 12 from each sides.

`-22-12<x+12-12<22-12`

`-34<x<10`

The solution of given inequality is
`-34<x<10`.