Question

1/3(y - 2) -5/6 (y + 1) =3/4 (y - 3) - 2

Answer 1

`y=(11)/(5)`

Explanation:

Given expression

`(1)/(3)(y-2)-(5)/(6)(y+1)=(3)/(4)(y-3)-2`

To solve for
`y` for the given expression.

Solution:

We multiply each term with the least common multiple of the denominators of the fraction in order to remove fractions.

The multiples of the denominators are:

3 = 3,6,9,12,15

6 = 6,12

4 = 4,8,12

The least common multiple = 12.

Multiplying each term with 12.

`12.(1)/(3)(y-2)-12.(5)/(6)(y+1)=12.(3)/(4)(y-3)-2(12)`

`4(y-2)-10(y+1)=9(y-3)-24`

Using distribution.

`4y-8-10y-10=9y-27-24`

Simplifying.

`-6y-18=9y-51`

Adding
`6y` both sides.

`-6y+6y-18=9y+6y-51`

`-18=15y-51`

Adding 51 both sides.

`-18+51=15y-51+51`

`33=15y`

Dividing both sides by 15.

`(33)/(15)=(15y)/(15)`

`(33)/(15)=y`

Simplifying fractions.

`(11)/(5)=y`

∴
`y=(11)/(5)` (Answer)