Question

Question #eda6e

Answer 1

`y=26`

Explanation:

`"eliminate the fractions by multiplying ALL terms by"`
`"12 the lowest common multiple of 3 and 4"`

`cancel(12)^4xx1/cancel(4)^1(y+4)+84=cancel(12)^3(3y-2)-24`

`rArr4(y+4)+84=3(2y-2)-24`

`"distribute brackets on both sides and collect like terms"`

`rArr4y+16+84=9y-6-24`

`rArr4y+100=9y-30`

`"subtract 9y from both sides"`

`4y-9y+100=cancel(9y)cancel(-6y)-30`

`rArr-5y+100=-30`

`"subtract 100 from both sides"`

`-5ycancel(+100)cancel(-100)=-30-100`

`rArr-5y=-130`

`"divide both sides by "-5`

`(cancel(-5) y)/cancel(-5)=(-130)/(-5)`

`rArry=26`

`color(blue)"As a check"`

Substitute this value into the equation and if both sides are equal then it is the solution.

`"left "=1/3(30)+7=10+7=17`

`"right "=1/4(76)-2=19-2=17`

`rArry=26" is the solution"`