To solve the equation \( 7(2a - 3) - 5v = -3 \), we start by distributing the \( 7 \) on the left side:
\[ 7 \cdot 2a - 7 \cdot 3 - 5v = -3 \]
This simplifies to:
\[ 14a - 21 - 5v = -3 \]
Next, we can isolate the \( v \) term by adding \( 21 \) to both sides:
\[ 14a - 5v = -3 + 21 \]
\[ 14a - 5v = 18 \]
Now, we can rearrange this equation to express \( v \) in terms of \( a \):
\[ -5v = 18 - 14a \]
Dividing by \(-5\):
\[ v = \frac{14a - 18}{5} \]
So, the solution for \( v \) in terms of \( a \) is:
\[ v = \frac{14a - 18}{5} \]