Question

Combine and Simplify:
48 (1/4x - 1/3y - 2/6x - 3/8y - 2/3
WRITE 2 WAYS!

Answer 1

Combining and simplifying
`48((1)/(4)x-(1)/(3)y-(2)/(6)x-(3)/(8)y-(2)/(3))` we get
`\mathbf{-4x-34y-32}` or we can write as
`\mathbf{48((-x)/(12) -(17y)/(24)- (2)/(3))}`

Explanation:

We need to combine and simplify

`48((1)/(4)x-(1)/(3)y-(2)/(6)x-(3)/(8)y-(2)/(3))`

First we will combine like terms and then perform the mathematical operations like addition or subtraction.

Like terms: terms having same variable

`48((1)/(4)x-(2)/(6)x-(1)/(3)y-(3)/(8)y-(2)/(3))`

Now we take LCM of like terms

`=48((1)/(4)x-(2)/(6)x-(1)/(3)y-(3)/(8)y-(2)/(3))\\=48((x*3-2x*2)/(12) +(-y*8-3y*3)/(24)- (2)/(3))\\=48((3x-4x)/(12) +(-8y-9y)/(24)- (2)/(3))\\=48((-x)/(12) +(-17y)/(24)- (2)/(3))\\=48((-x)/(12) -(17y)/(24)- (2)/(3))`

Now, we can multiply 48 with terms inside the bracket.

we can simplify the terms if they are both divisible by same number.

`=48((-x)/(12) -(17y)/(24)- (2)/(3))\\=48((-x)/(12) )-48((17y)/(24))-48((2)/(3)))\\=-4x-34y-32`

So, Combining and simplifying
`48((1)/(4)x-(1)/(3)y-(2)/(6)x-(3)/(8)y-(2)/(3))` we get
`\mathbf{-4x-34y-32}` or we can write as
`\mathbf{48((-x)/(12) -(17y)/(24)- (2)/(3))}`