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How do you solve #abs(7-y)=4#?

Answer 1

y = 3 and y = 11

Because we are taking the absolute value of #7-y#, we set up two equations that correspond to the negative and positive outcomes of #|7-y|#

#7-y = 4# and #-(7-y) = 4#

This is because the answer to both equations when taken as absolute values is the same, so all we have to do is solve for y in each case.

#7-y=4; y = 3#

and

#-7+y=4; y = 11#

To illustrate this, we can enter both values into the original function.

#|7-(3)| = 4#

#|7-(11)|=4#

Both scenarios are real, and there are two ways to handle y.

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Answer 2

Jace Anderson

To solve the absolute value equation ( \text{abs}(7 - y) = 4 ), you consider two cases:

( 7 - y = 4 )
( 7 - y = -4 )

For the first case: [ 7 - y = 4 ] [ -y = 4 - 7 ] [ -y = -3 ] [ y = 3 ]

For the second case: [ 7 - y = -4 ] [ -y = -4 - 7 ] [ -y = -11 ] [ y = 11 ]

So the solutions to the equation are ( y = 3 ) and ( y = 11 ).

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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.