Question

Which expression is equivalent to

2/3(9x-6)+4(1/2 x -- 1/2)


1/2 and 3/4 are fractions

Answer 1

Given expression
`(2)/(3)(9x-6)+4((1)/(2)x-(1)/(2))` is equivalent to the expression
`2(4x-3)`.

Explanation:

Given expression is
`(2)/(3)(9x-6)+4((1)/(2)x-(1)/(2))`

To simplify the expression:

`(2)/(3)(9x-6)+4((1)/(2)x-(1)/(2))=(18x-12)/(3)+(4x-4)/(2)`

Taking LCM 6 to the above expression we get

`=((18x-12)2+3(4x-4))/(6)` (Applying multiplication rules)

`=(36x-24+12x-12)/(6)` ( doing sums to the terms)

`=(48x-36)/(6)`

`=8x-6`

We can take common number 2 outside to the above expression

`=2(4x-3)`

Therefore
`(2)/(3)(9x-6)+4((1)/(2)x-(1)/(2))=2(4x-3)`

Therefore given expression
`(2)/(3)(9x-6)+4((1)/(2)x-(1)/(2))` is equivalent to the expression
`2(4x-3)`.