Question

What is y in the equation 2/3 (2y+1) = 3/7 (2-y)

Answer 1

first u have to distribute

4/3y+2/3= 6/7-3/7y

now subtract 2/3 on both sides

4/3y+2/3-2/3=6/7- 2/3-3/7y

4/3y= 6/7- 2/3-3/7y

u need to have common denominator

-2/3= - 14/21

6/7=18/21

18/21-14/21= 4/21

4/3y=4/21-3/7y

add 3/7y to both sides

u need to have common denominator

4/3y= 28/21y

3/7y= 9/21y

28/21y+9/21y= 37/21y

37/21y= 4/21

multiply 21/37 to both sides

37/21y times 21/37= 4/21 times 21/37

• y=84/777
• y= 9/111
• y=3/37

Answer 2

`y=(4)/(37)`

Explanation:

`(2)/(3)(2y+1)=(3)/(7)(2-y)`

`(4)/(3)y+(2)/(3) =(6)/(7)- (3)/(7)y`

Add
`(3)/(7)y` on both sides and subtract
`(2)/(3)` on both sides.

`((3)/(7)y- (2)/(3))+(4)/(3)y+(2)/(3) =(6)/(7)- (3)/(7)y+((3)/(7)y- (2)/(3))`

`(3)/(7)y+(4)/(3)y=(6)/(7)-(2)/(3)`

Solve the fractions.

`((3)(3)+(7)(4))/((7)(3))y=((6)(3)-(7)(2))/((7)(3))`

`(9+28)/(21) y=(18-14)/(21)`

`(37)/(21)y =(4)/(21)`

Multiply by the reciprocal of the fraction with the variable to isolate the variable. The reciprocal is the inverted fraction.

`(21)/(37)*(37)/(21)y =(4)/(21)*(21)/(37)`

`y=(4)/(37)`