Question

What is the solution to the inequality

Answer 1

Answer:

p > 5 and p <-8

Step-by-step explanation:

To solve this, you first need to isolate p.

First add 6 on both sides of the equation:

$-6 + |2p+3| >7\\\\(+6) -6 + |2p+3| >7 +6\\\\2p + 3 > 13$

Then subtract 3 from both sides of the equation.

$2p+3-3>13-3\\\\2p > 10$

The divide both sides by 2.

$\dfrac{2p}{2}>\dfrac{10}{2}\\\\p>5$

Another solution is possible because of the absolute value.

If $|2p+3|>13$

Then $|2p+3|<-13$

Thus we can solve the second solution:

$|2p+3|<-13$

$2p+3<-13$

Isolate P again by subtracting both sides by 3

$2p+3-3<-13-3$

$2p<-16$

Then divide both sides by 2:

$\dfrac{2p}{2}<-\dfrac{16}{2}$

$p<-8$

Answer 2

Answer:

p > 5, p < -8

Step-by-step explanation:

We are given the following inequality and we are to find its solution:

$-6+|2p+3|>7$

Adding 6 to both sides to get:

$-6+6+|2p+3|>7+6$

$|2p+3|>13$

We know the absolute rule that $\mathrm{If}\:|u|\:>\:a,\:a>0\:\mathrm{then}\:u\:<\:-a\:\quad \mathrm{or}\quad \:u\:>\:a$.

So $2p+3>13$ or $2p+3<-13$

$2 p > 1 3 - 3$, $2 p < - 1 3 - 3$

$2 p > 1 0$, $2 p < - 1 6$

$p>\frac{10}{2}$, $p<\frac{-16}{2}$

p > 5, p < -8