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

Answer:

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

Step-by-step explanation:

The original expression in this problem is

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

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

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

So we get:

$\frac{5}{3}x+35-\frac{3}{2}x+12$

Now we can rewrite this using mixed fractions:

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

Which can be also written as

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

And finally, by solving it, we find

$\frac{1}{6}x+47$ (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