Question

-4|6b-8|<12 pls help so confused

Answer 1

b > 5/6 or b < 11/6

Explanation:

1. Divide both sides by -4

`(-4(|6b-8|))/(-4) < (12)/(-4)`

2. Simplify above

`|6b-8| > -3`

3. The absolute value of an expression means that the expression can be positive or negative
Here | | represents the absolute value of 6b-8

For an absolute value to satisfy the above inequality
either 6b - 8 > -3 or 6b - 8 < - (-3)

(This follows from the fact that if |x| > -a, x > -a
or x < -(-a) ) which is the same as x < a

First case: 6b - 8 > -3:

6b - 8 + 8 > -3 + 8 ( Add 8 to both sides)
==> 6b > 5
==> 6b/6 > 5/6 (Divide both sides by 6)
==> b > 5/6

Second case: 6b - 8 < 3
6b −8 + 8 <3 + 8 (Add 8 to both sides)
==> 6b<11

==> 6b/6 < 11/6 (Divide both sides by 6)

==> b < 11/6