Answer:
[tex] - \frac{9}{4} < p < \frac{5}{4} [/tex]
Step-by-step explanation:
1) Subtract 8 from both sides.
[tex] - 6 |4p + 2| > - 34 -8[/tex]
2) Simplify -34 - 8 to -42.
[tex] - 6 |4p + 2| > - 42[/tex]
3) Divide both sides by -6.
[tex] |4p + 2| < \frac{ - 42}{ - 6} [/tex]
4) Two negative numbers makes a positive.
[tex] |4p + 2| < \frac{42}{6} [/tex]
5) Simplify 42/6 to 7.
[tex] |4p + 2| < 7[/tex]
6) Rewrite the inequality without the absolute value.
[tex] - 7 < 4p + 2 < 7[/tex]
7) Subtract 2 from the whole equation.
[tex] - 7 - 2 < 4p < 7 - 2[/tex]
8) Simplify.
[tex] - 9 < 4p < 5[/tex]
9) Divide the whole equation by 4.
[tex] - \frac{9}{4} < p < \frac{5}{4} [/tex]
Therefor, the answer is - 9/4 < p < 5/4.
