To solve the equation \( 5(15v - 10) = 8v + 8 \), we will first use the distributive property to eliminate the parentheses on the left side of the equation.
Step 1: Distribute the 5
\[ 5(15v - 10) = 5 \cdot 15v - 5 \cdot 10 \] This simplifies to: \[ 75v - 50 \]
Step 2: Rewrite the equation
Now the equation can be rewritten as: \[ 75v - 50 = 8v + 8 \]
Step 3: Get all \( v \) terms on one side and constant terms on the other side
Subtract \( 8v \) from both sides: \[ 75v - 8v - 50 = 8 \] This simplifies to: \[ 67v - 50 = 8 \]
Next, add 50 to both sides: \[ 67v = 8 + 50 \] This simplifies to: \[ 67v = 58 \]
Step 4: Solve for \( v \)
Now, divide both sides by 67: \[ v = \frac{58}{67} \]
Thus, the value of \( v \) is: \[ \boxed{\frac{58}{67}} \]