Question

Which expressions are equivalent to 5 (one-third x + 7) minus 3 (one-half x minus 4)? Select three options.

5 and one-third x minus 3 and one-half x + 35 minus 12
One-sixth x + 47
1 and two-thirds x + 35 minus 1 and one-half x + 12
5 (one-third x) + (5) (7) minus (3) (one-half x) + (3) (4)
1 and one-third x + 35 minus 1 and one-half x minus 12

Answer 1

One-sixth x + 47

1 and two-thirds x + 35 minus 1 and one-half x + 12

1 and one-third x + 35 minus 1 and one-half x minus 12

Explanation:

The original expression in this problem is

`5((1)/(3)x+7)-3((1)/(2)x-4)`

We start by applying the distributive property and multiplying each factor outside the brackets by each factor inside:

`5\cdot (1)/(3)x+5\cdot 7 -3\cdot (1)/(2)x+3\cdot 4`

So we get:

`(5)/(3)x+35-(3)/(2)x+12`

Now we can rewrite this using mixed fractions:

`1(2)/(3)x+35-1(1)/(2)x+12` (1)

Which can be also written as

`1(2)/(3)x+35-(1(1)/(2)x-12)` (2)

And finally, by solving it, we find

`(1)/(6)x+47` (3)

So the three correct options are

One-sixth x + 47

1 and two-thirds x + 35 minus 1 and one-half x + 12

1 and one-third x + 35 minus 1 and one-half x minus 12