Question

Simplify the expression. Show your calculations. (2 points) (7.EE.1) 1/3(6 − 12y) + 1/4(24y + 14)

Answer 1

To simplify the expression \( \frac{1}{3}(6 - 12y) + \frac{1}{4}(24y + 14) \), we will first distribute the constants and then combine like terms.

1. Distribute \( \frac{1}{3} \) to \( (6 - 12y) \):
\[
\frac{1}{3}(6) - \frac{1}{3}(12y) = 2 - 4y
\]

2. Distribute \( \frac{1}{4} \) to \( (24y + 14) \):
\[
\frac{1}{4}(24y) + \frac{1}{4}(14) = 6y + \frac{14}{4}
\]
Simplifying \( \frac{14}{4} \) gives:
\[
\frac{14}{4} = \frac{7}{2}
\]

So we have:
\[
\frac{1}{4}(24y + 14) = 6y + \frac{7}{2}
\]

3. Now combine the two results:
\[
2 - 4y + 6y + \frac{7}{2}
\]

4. Combine like terms:
For the \( y \) terms:
\[
-4y + 6y = 2y
\]

So the expression now looks like this:
\[
2y + 2 + \frac{7}{2}
\]

5. To combine the constant terms \( 2 \) and \( \frac{7}{2} \):
Convert \( 2 \) into a fraction with a denominator of 2:
\[
2 = \frac{4}{2}
\]

Now add \( \frac{4}{2} + \frac{7}{2} \):
\[
\frac{4 + 7}{2} = \frac{11}{2}
\]

6. Now put it all together:
\[
2y + \frac{11}{2}
\]

Thus, the simplified expression is:
\[
\boxed{2y + \frac{11}{2}}
\]