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What is the solution to the inequality

What is the solution to the inequality-example-1

2 Answers

2 votes

Answer:

p > 5, p < -8

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>(10)/(2),
p<(-16)/(2)

p > 5, p < -8

User Alex Dzeshko
by
7.6k points
5 votes

Answer:

p > 5 and p <-8

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.


(2p)/(2)>(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:


(2p)/(2)<-(16)/(2)


p<-8

User Piyush Bhati
by
8.0k points

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