-3 l -8p - 9 l = -15

To solve first we need to isolate the absolute value one one side:

Let us divide by -3:

==?> l -8p - 9 l = 5

Now we have two possible solutions:

1) ( -8p -9) = 5

==> add 9 to both sides:

==> -8p = 14

Now divide by -8

==> p = -14/8 = -7/4

==> p1= -7/4

2. -(-8p-9) = 5

==> 8p + 9 = 5

==> Subtract 9 from both sides:

==> 8p = -4

Now divide by 8:

==> p = -1/2

==> we have two aolutions:

**p = { -1/2 , -7/4}**

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.