Question

Solve the inequality |8x + 4| <28
need answered fast!!!

Answer 1

4<x< 3

Explanation:

Answer 2

The absolute value
`|x|` always returns the "positive version" of a number.

This means that if the number is positive, the absolute value does nothing:

`|x| = x`

And if the number is negative, the absolute value flips its sign:

`|x| = -x`

So, if 8x+4 is positive, the inequality becomes

`8x+4 < 28`

If 8x+4 is negative, the inequality becomes

`-8x-4 < 28 \iff 8x+4 > -28`

So, 8x+4 must be either a positive number smaller than 28, or a negative number greater than -28. It means that

`-28 < 8x+4 < 28`

Subtract 4 from all sides:

`-32 < 8x < 24`

Divide all sides by 8:

`-4 < x < 3`