Question 502905: 3(2y-8)+2=5-2(y-4)-3
Answer by persian52(161)   (Show Source):
You can put this solution on YOUR website! 3(2y-8)+2=5-2(y-4)-3
Since 2 does not contain the variable to solve for, move it to the right-hand side of the equation by subtracting 2 from both sides.
3(2y-8)=-2+5-2(y-4)-3
Multiply -2 by each term inside the parentheses (y-4).
3(2y-8)=-2+5+(-2(y)-2(-4))-3
Multiply -2 by the y inside the parentheses.
3(2y-8)=-2+5+(-2*y-2(-4))-3
Multiply -2 by y to get -2y.
3(2y-8)=-2+5+(-2y-2(-4))-3
Multiply -2 by the -4 inside the parentheses.
3(2y-8)=-2+5+(-2y+2*4)-3
Multiply 2 by 4 to get 8.
3(2y-8)=-2+5+(-2y+8)-3
Remove the parentheses around the expression -2y+8.
3(2y-8)=-2+5-2y+8-3
Add 5 to -2 to get 3.
3(2y-8)=3-2y+8-3
Add 8 to 3 to get 11.
3(2y-8)=11-2y-3
Subtract 3 from 11 to get 8.
3(2y-8)=8-2y
Reorder the polynomial 8-2y alphabetically from left to right, starting with the highest order term.
3(2y-8)=-2y+8
Multiply 3 by each term inside the parentheses (2y-8).
(3(2y)+3(-8))=-2y+8
Multiply 3 by the 2y inside the parentheses.
(3*2y+3(-8))=-2y+8
Multiply 3 by 2y to get 6y.
(6y+3(-8))=-2y+8
Multiply 3 by the -8 inside the parentheses.
(6y-3*8)=-2y+8
Multiply -3 by 8 to get -24.
(6y-24)=-2y+8
Remove the parentheses around the expression 6y-24.
6y-24=-2y+8
Since -2y contains the variable to solve for, move it to the left-hand side of the equation by adding 2y to both sides.
6y-24+2y=8
According to the distributive property, for any numbers a, b, and c, a(b+c)=ab+ac and (b+c)a=ba+ca. Here, y is a factor of both 6y and 2y.
(6+2)y-24=8
Add 2 to 6 to get 8.
(8)y-24=8
Remove the parentheses.
8y-24=8
Since -24 does not contain the variable to solve for, move it to the right-hand side of the equation by adding 24 to both sides.
8y=24+8
Add 8 to 24 to get 32.
8y=32
Divide each term in the equation by 8.
(8y)/(8)=(32)/(8)
Cancel the common factor of 8 in (8y)/(8).
(8y)/(8)=(32)/(8)
Remove the common factors that were cancelled out.
y=(32)/(8)
Cancel the common factor of 8 in (32)/(8).
y=(^(4)32)/(8)
Remove the common factors that were cancelled out.
y=4
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