# Determine P value in the following equation:-3 l -8p - 9 l = -15.

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-3|-8p-9|=-15

Divide by -3:

|-8p-9|=5

Since we are dealing with absolute values there are 2 possibilities:

-8p-9=5 (1)

-8p-9=-5 (2)

Lets solve (1) first:

-8p-9=5

-8p=14

p=14/-8 = -7/4

Now let's solve (2):

-8p-9=-5

-8p=4

p=4/-8 = -1/2

**The 2 possible values of p are -7/4 and -1/2.**

We'll explain the modulus:

-8p - 9 for -8p - 9>=0

-8p>=9

p>=-9/8

p belongs to the interval [-9/8 , +infinite)

8p + 9 for p<-9/8

p belongs to the interval (-infinite, -9/8)

1) We'll solve the equation for p belongs to the interval [-9/8 , +infinite).

-3 (-8p - 9 ) = -15

We'll divide by -3:

-8p - 9 = 5

-8p = 9+5

-8p = 14

p = -14/8

p = -7/4 < -9/8

The solution p = -7/4 is rejected since it doues not belong to the interval of admissible values.

2) We'll solve the equation for p belongs to the interval (-infinite, -9/8).

8p + 9 = 5

8p = -4

p = -1/2 > -9/8

Again, the solution will be rejected.