Question

(Absolute value inequalities) 50 points!

-6|4p+2|+8 > -34

Answer 1

`- (9)/(4) < p < (5)/(4)`

Explanation:

1) Subtract 8 from both sides.

`- 6 |4p + 2| > - 34 -8`

2) Simplify -34 - 8 to -42.

`- 6 |4p + 2| > - 42`

3) Divide both sides by -6.

`|4p + 2| < ( - 42)/( - 6)`

4) Two negative numbers makes a positive.

`|4p + 2| < (42)/(6)`

5) Simplify 42/6 to 7.

`|4p + 2| < 7`

6) Rewrite the inequality without the absolute value.

`- 7 < 4p + 2 < 7`

7) Subtract 2 from the whole equation.

`- 7 - 2 < 4p < 7 - 2`

8) Simplify.

`- 9 < 4p < 5`

9) Divide the whole equation by 4.

`- (9)/(4) < p < (5)/(4)`

Therefor, the answer is - 9/4 < p < 5/4.

Answer 2

p>5/4 or p<-9/4

Explanation:

1. first isolate the absolute value by subtracting 8 and then dividing by -6

2. you then split the absolute value inequality into 4p+2>7 and 4p+2<-7

3. When you solve those, you get p>5/4 and p< -9/4