Question

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

Answer 1

Answer:

b,c,e

Step-by-step explanation: These are the answers from the dude above me

Answer 2

Answer:

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

$5(\frac{1}{3}x+7)-3(\frac{1}{2}x-4)$

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:

$=5\cdot \frac{1}{3}x + 5\cdot 7 - 3\cdot \frac{1}{2}x + 3 \cdot 4 =\\=\frac{5}{3}x+35 -\frac{3}{2}x+12$

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

$=1\frac{2}{3}x+35-1\frac{1}{2}x+12$

Also as

$=(1\frac{2}{3}x+35)-(1\frac{1}{2}x-12)$

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

$=(\frac{5}{3}x-\frac{3}{2}x)+(35+12)=\\=\frac{1}{6}x+47$

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