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

Answer 1

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

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#.

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Answer 2

Genesis Allen

To solve the equation abs(6n + 1) = 1/2, you need to consider both the positive and negative cases of the absolute value expression:

Positive case: 6n + 1 = 1/2

Negative case: -(6n + 1) = 1/2

Solve each equation separately to find the values of n.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.