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

1 Answer
Jun 14, 2017

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.