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

Question

Isaiah Anthony · Accepted Answer

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

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)#. We need to solve both equations in order to get the answer. 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#.

Isaiah Anthony · Answer

#p=-1,-1/3#

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#

First, solve the 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#

Work out 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#

Eva Adamson · Answer

undefined To solve the equation $|9p + 6| = 3$, you need to consider two cases:

Case 1: $9p + 6 = 3$  
   Solve for $p$ in this case.

Case 2: $9p + 6 = -3$  
   Solve for $p$ in this case.

After finding solutions for both cases, you will have your final solution set.