what is the solution to the inequality -6+|2p + 3|>7?\n p < -8 or p > 5\n -8 < p < 5\n p < -2 or p > -1\n -2…

what is the solution to the inequality -6+|2p + 3|>7?\n p < -8 or p > 5\n -8 < p < 5\n p < -2 or p > -1\n -2 > p > -1

what is the solution to the inequality -6+|2p + 3|>7?\n p < -8 or p > 5\n -8 < p < 5\n p < -2 or p > -1\n -2 > p > -1

Answer

Explanation:

Step1: Isolate the absolute - value expression

Add 6 to both sides of the inequality $-6 + |2p + 3|>7$. $|2p + 3|>7 + 6$, so $|2p+3|>13$.

Step2: Consider two cases

Case 1: $2p + 3>13$. Subtract 3 from both sides: $2p>13 - 3$, so $2p>10$. Divide both sides by 2: $p > 5$. Case 2: $2p+3<-13$. Subtract 3 from both sides: $2p<-13 - 3$, so $2p<-16$. Divide both sides by 2: $p<-8$.

Answer:

$p < - 8$ or $p>5$