Question

How do you solve `\frac { 9y + 8} { 4} = \frac { 3y + 5} { 2} + 7`?

Answer 1

`y = 10`

Explanation:

`(9y+8)/4 = (3y+5)/2+7" "` Multiply both sides by 4

`9y+8 = 4((3y+5)/2+7)`

`9y+8 = 2(3y+5)+28`

`9y+8 = 6y+10+28`

`9y-6y = 38-8`

`3y = 30`

`y = 30/3`

`y = 10`

hope that helped

:-)

Answer 2

`y=10`

Explanation:

To eliminate the fractions in the equation, multiply ALL terms on both sides by the `color(blue)"lowest common multiple"` ( LCM ) of 4 and 2, the denominators of the fractions.

The LCM of 4 and 2 is 4

`(cancel(4)^1xx(9y+8)/cancel(4)^1)=(cancel(4)^2xx(3y+5)/cancel(2)^1)+(4xx7)`

`rArr9y+8=2(3y+5)+28`

distribute bracket.

`9y+8=6y+10+28`

`rArr9y+8=6y+38`

subtract 6y from both sides.

`9y-6y+8=cancel(6y)cancel(-6y)+38`

`rArr3y+8=38`

subtract 8 from both sides.

`3ycancel(+8)cancel(-8)=38-8`

`rArr3y=30`

divide both sides by 3

`(cancel(3) y)/cancel(3)=30/3`

`rArry=10`

`color(blue)"As a check"`

Substitute this value into the equation and if the left side equals the right side then it is the solution.

`"left side "=((9xx10)+8)/4=98/4=24.5`

`"right side "=((3xx10)+5)/2+7=35/2+7=24.5`

`rArry=10" is the solution"`