How do I solve the inequality 6|p|+8>-22? It's a multiple choice question on my homework and the answers available are either
:
A) {All real numbers}
B) -5 < p < 5
2 answers:
6|p|+8 > - 22 ; could be written :
|6.p| + 8 > - 22. Now subtract 8 to both sides
|6p| +8 -8>-22 -8 → |6p| > - 30 . Divide both sides by 6:
|p| > - 5
Clearing the absolute value bars yields:
p> - 5 and p< 5 (remember |x| = a → x = +a and x = -a)
Then :
- 5< p < +5
------------------------(-5)---------------------0--------------------(+5)----------------------
∅============(P)============∅

Subtract 8.

Divide by 6.

The solution set is all real numbers because no matter what number is chosen for p, its absolute value will be bigger than any negative number.
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