Question: Complete the equation so that it has infinitely many solutions. Enter the answers.
$\frac{1}{6} (36v + 24) - v = \text{[blank]} v + \text{[blank]}$
1. **State the problem:** We want to complete the equation
$$\frac{1}{6} (36v + 24) - v = \text{[blank]} v + \text{[blank]}$$
so that it has infinitely many solutions.
2. **Recall the rule for infinitely many solutions:**
An equation has infinitely many solutions if both sides are identical expressions for all values of $v$.
3. **Simplify the left side:**
$$\frac{1}{6} (36v + 24) - v = \frac{1}{6} \times 36v + \frac{1}{6} \times 24 - v = 6v + 4 - v$$
Simplify further:
$$6v + 4 - v = 5v + 4$$
4. **Set the right side equal to the simplified left side:**
$$\text{[blank]} v + \text{[blank]} = 5v + 4$$
5. **Therefore, the blanks are:**
$$\boxed{5} \text{ and } \boxed{4}$$
6. **Final equation:**
$$\frac{1}{6} (36v + 24) - v = 5v + 4$$
This equation has infinitely many solutions because both sides simplify to the same expression.