Question

Simplify the expression. Write your answers using integers or improper fractions.
3, left parenthesis, minus, 3, u, minus, 4, right parenthesis, plus, start fraction, 2, divided by, 5, end fraction, u
3(−3u−4)+
5
2
​
u

Answer 1

To simplify the expression \( 3(-3u - 4) + \frac{2}{5}u \), let's follow these steps:

1. Distribute the 3 in the first term:
\[
3(-3u) + 3(-4) = -9u - 12
\]

2. Now, rewrite the expression:
\[
-9u - 12 + \frac{2}{5}u
\]

3. Combine the \( u \) terms. We need to express \(-9u\) with a common denominator to combine with \(\frac{2}{5}u\). The common denominator between 1 and 5 is 5:
\[
-9u = -\frac{45}{5}u
\]

4. Now combine the \( u \) terms:
\[
-\frac{45}{5}u + \frac{2}{5}u = \frac{-45 + 2}{5}u = \frac{-43}{5}u
\]

5. Now, write the entire simplified expression:
\[
\frac{-43}{5}u - 12
\]

So, the final simplified result is:
\[
\frac{-43}{5}u - 12
\]