Question

(Absolute value inequalities) 50 points! -6|4p+2|+8 > -34

Answer 1

Answer:

$- \frac{9}{4} < p < \frac{5}{4}$

Step-by-step 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.

$|4p + 2| < \frac{ - 42}{ - 6}$

4) Two negative numbers makes a positive.

$|4p + 2| < \frac{42}{6}$

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.

$- \frac{9}{4} < p < \frac{5}{4}$

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

Answer 2

Answer

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

Step-by-step 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