To apply the distributive property and rewrite the expression \( 5(15v - 10) \):
- Distribute the \( 5 \) to both terms inside the parentheses:
\[ 5(15v) - 5(10) \]
- Calculate each term:
\[ 75v - 50 \]
Now the equation \( 5(15v - 10) = 8v + 8 \) becomes:
\[ 75v - 50 = 8v + 8 \]
Next, to isolate \( v \):
- Get all the \( v \) terms on one side. Subtract \( 8v \) from both sides:
\[ 75v - 8v - 50 = 8 \]
This simplifies to:
\[ 67v - 50 = 8 \]
- Next, add \( 50 \) to both sides to isolate the term with \( v \):
\[ 67v = 8 + 50 \]
Which simplifies to:
\[ 67v = 58 \]
- Finally, divide both sides by \( 67 \) to solve for \( v \):
\[ v = \frac{58}{67} \]
So the solution for \( v \) is:
\[ v = \frac{58}{67} \]