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How do you solve for y in #3+6x = 11-4y#?

Answer 1

See the entire solution process below:

First, subtract #color(red)(11)# from each side of the equation to isolate the #y# term while keeping the equation balanced:

#-color(red)(11) + 3 + 6x = -color(red)(11) + 11 - 4y#

#-8 + 6x = 0 - 4y#

#-8 + 6x = -4y#

Now, divide each side of the equation by #color(red)(-4)# to solve for #y# while keeping the equation balanced:

#(-8 + 6x)/color(red)(-4) = (-4y)/color(red)(-4)#

#(-8)/color(red)(-4) + (6x)/color(red)(-4) = (color(red)(cancel(color(Black)(-4)))y)/cancel(color(red)(-4))#

#2 - 6/4x = y#

#2 - (2 xx 3)/(2 xx 2)x = y#

#2 - (color(red)(cancel(color(black)(2))) xx 3)/(color(red)(cancel(color(black)(2))) xx 2)x = y#

#2 - 3/2/x = y#

#y = 2 - 3/2x#

#y = -3/2x + 2#

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Answer 2

Nathan Axel

To solve for ( y ), first, isolate the term with ( y ) on one side of the equation:

[ 3 + 6x = 11 - 4y ]

[ 4y = 11 - 3 - 6x ]

[ 4y = 8 - 6x ]

Then, divide both sides by 4 to solve for ( y ):

[ y = \frac{8 - 6x}{4} ]

[ y = 2 - \frac{3}{2}x ]

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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.