How do you solve #abs(6n+1)=1/2#?

1 Answer
Jun 14, 2017

Answer:

#n=-1/12# and #n=-1/4#

Explanation:

Since absolute value bars are involved, you know that the quantity #(6n+1)# *within the bars will always end up positive.*

Therefore, #(6n+1)# can be equal to #1/2# OR #-1/2#. There are two possible solutions for n.

You must set up and solve 2 separate equations to solve for the positive and negative versions.
First Equation: quantity in absolute value bars equal to #1/2#.
#(6n+1)=1/2# [Solve]
#n=-1/12#
Second Equation: quantity in absolute value bars equal to #-1/2#.
#(6n+1)=-1/2# [Solve]
#n=-1/4#

Both #-1/12# and #-1/4# are solutions to #|6n+1|=1/2#.

If you want to check your work, SEPARATELY substitute these solutions for #n# into the original equation, #|6n+1|=1/2#.