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

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

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

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

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

If 8x+4 is negative, the inequality becomes

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

Subtract 4 from all sides:

Divide all sides by 8: