Question

Solve for v.
1/2v+8=3–1/3v
v=

Answer 1

To solve the equation \( \frac{1}{2}v + 8 = 3 - \frac{1}{3}v \), we first want to eliminate the fractions by finding a common denominator. The least common multiple of 2 and 3 is 6.

Let's multiply every term in the equation by 6:

\[
6 \left( \frac{1}{2}v \right) + 6 \cdot 8 = 6 \cdot 3 - 6 \left( \frac{1}{3}v \right)
\]

This simplifies to:

\[
3v + 48 = 18 - 2v
\]

Next, we will add \( 2v \) to both sides to combine the \( v \) terms:

\[
3v + 2v + 48 = 18
\]

This simplifies to:

\[
5v + 48 = 18
\]

Now, subtract 48 from both sides:

\[
5v = 18 - 48
\]

This simplifies to:

\[
5v = -30
\]

Finally, divide by 5 to solve for \( v \):

\[
v = \frac{-30}{5}
\]

Thus, we find:

\[
v = -6
\]

The solution is:

\[
\boxed{-6}
\]