How do you solve #6y - 8 = 12 + 10y#?

Answer 1

Expanded explanation

#color(red)("Objective is to have y, on its own, on one side of the = and everything else on the other side.")#

Brackets are used to show previous part to help make things clearer about what is happening.

.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

#color(blue)("Add 8 to both sides to remove it from the left.")#
#(6y-8) + color(red)(8) = (12 + 10y) + color(red)(8)#
#6y -8 + 8 = 12 +8 + 10y#
#6y +0 = 20 + 10y#
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ #color(blue)("Subtract 10y from both sides to remove it from the right.")#
#(6y) - color(red)(10y) = (20+10y)-color(red)(10y)#
#6y - color(red)(10y) = 20+10y-color(red)(10y)#
#-4y = 20#

We need the y part to be positive so multiply both sides by negative 1

# color(red)(-1) times (-4y) = color(red)(-1) times (20)#
#4y =-20#
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ #color(blue)("Divide both sides by 4 so that the 4 in front of 4y becomes 1. As 1 times anything is itself.")#
#color(red)(1/4) times (4y) = color(red)(1/4) times (-20)#
#1 times y = (-20)/4#
#y= - 5#
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Answer 2

To solve the equation 6y - 8 = 12 + 10y:

  1. Subtract 6y from both sides: -8 = 12 + 4y.
  2. Subtract 12 from both sides: -20 = 4y.
  3. Divide both sides by 4: y = -5.
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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.

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.

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.

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.

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