How do you solve #abs(9p+6)=3#?

2 Answers
May 11, 2018

Answer:

#p# can equal #-1/3# or #-1#.

Explanation:

An absolute value, indicated by #||#, means that you use the number's distance from zero. In other words, the number becomes positive. For example, #|-1|# and #|1|# both equal #1#, because both are #1# away from zero.

Both the negative and positive forms of a number equal the same thing in absolute value form. This means that #3=9p+6# or #3=-(9p+6)#.

To find the answer, we must solve both equations.

First, #3=9p+6#. We need to isolate the variable and then simplify.

#3-6=9p#
#-3=9p#
#-3/9=p#
#-1/3=p#

Next, #3=-(9p+6)#. We must distribute the negative, and then isolate and simplify.

#3=-9p-6#
#3+6=-9p#
#9=-9p#
#9/-9=p#
#-1=p#

Therefore, #p# can equal #-1/3# or #-1#.

May 11, 2018

Answer:

#p=-1,-1/3#

Explanation:

Solve:

#abs(9p+6)=3#

Since #absa=a# and #abs(-a)=a#, we can break the given equation into two equations:

#9p+6=3# and #-(9p+6)=3#

Solve the first equation.

#9p+6=3#

Subtract #6# from both sides.

#9p+6-6=3-6#

#9p=-3#

Divide both sides by #9#.

#p=-3/9#

Simplify.

#p=-1/3#

Solve the second equation.

#-(9p+6)=3#

Expand.

#-9p-6=3#

Add #6# to both sides.

#-9p-6+6=3+6#

#-9p=9#

Divide both sides by #-9#.

#p=-9/9#

Simplify.

#p=-1#

#p=-1,-1/3#