Question

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

Answer 1

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:

$-4 < x < 3$