Question

When 2(3/5 x + 2/3 y - 1/4 x -1 1/2 y + 3 )is simplified, what is the resulting expression?

Answer 1

Simplifying the expression:
`2((3)/(5)x+(2)/(3)y-(1)/(4)x-1(1)/(2)y +3)` we get
`\mathbf{42x-100y-360}`

Explanation:

We need to simplify the expression:
`2((3)/(5)x+(2)/(3)y-(1)/(4)x-1(1)/(2)y +3)`

First we will solve terms inside the bracket

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

Converting mixed fraction
`1(1)/(2) y` into improper fraction, we get:
`(3)/(2)y`

Replacing the term:

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

Now, taking LCM of: 5,3,4,2 we get 60

Now multiply 60 with each term inside the bracket

`2((3)/(5)x*60+(2)/(3)y*60-(1)/(4)x*60-(3)/(2)y*60 +3*60)\\2(3x*12+2y*20-1x*15-3x*30-3*60)\\2(36x+40y-15x-90y-180)`

Now, combine like terms

`2(36x-15x-90y+40y-180)\\2(21x-50y-180)`

Now, multiply all terms with 2

`42x-100y-360`

So, Simplifying the expression:
`2((3)/(5)x+(2)/(3)y-(1)/(4)x-1(1)/(2)y +3)` we get
`\mathbf{42x-100y-360}`