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

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

One-sixth x + 47

Step-by-step explanation:

The original expression in the problem is

We need to expand this expression. First, we apply the distributive property and we multiply each of the numbers outside the bracket by each term in the brackets:

Now we can rewrite this expression in several ways. For instance, we can rewrite the two fractions as mixed fractions, and we get:

Also as

And now we add together the similar terms (those in x and those without x), and we  find:

So the three options are

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

One-sixth x + 47

the first option is the answer.