Question
Evaluate the expression for u = –1 and v = 5. Simplify your answer.
uv + 6v + u
3
=
uv + 6v + u
3
=
Answers
GPT-4o mini
To evaluate the expression \( \frac{uv + 6v + u}{3} \) for \( u = -1 \) and \( v = 5 \), we start by substituting the values of \( u \) and \( v \) into the expression.
First, we find \( uv \):
\[
uv = (-1)(5) = -5
\]
Next, we calculate \( 6v \):
\[
6v = 6(5) = 30
\]
Then we simply have \( u \):
\[
u = -1
\]
Now we can substitute \( uv \), \( 6v \), and \( u \) back into the expression:
\[
uv + 6v + u = -5 + 30 - 1
\]
Calculating inside the parentheses:
\[
-5 + 30 = 25
\]
Then:
\[
25 - 1 = 24
\]
Now we substitute this result back into the original expression:
\[
\frac{uv + 6v + u}{3} = \frac{24}{3} = 8
\]
Thus, the simplified answer is:
\[
\boxed{8}
\]
First, we find \( uv \):
\[
uv = (-1)(5) = -5
\]
Next, we calculate \( 6v \):
\[
6v = 6(5) = 30
\]
Then we simply have \( u \):
\[
u = -1
\]
Now we can substitute \( uv \), \( 6v \), and \( u \) back into the expression:
\[
uv + 6v + u = -5 + 30 - 1
\]
Calculating inside the parentheses:
\[
-5 + 30 = 25
\]
Then:
\[
25 - 1 = 24
\]
Now we substitute this result back into the original expression:
\[
\frac{uv + 6v + u}{3} = \frac{24}{3} = 8
\]
Thus, the simplified answer is:
\[
\boxed{8}
\]