Question

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

Answer 1

`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`.