1. **State the problem:** Solve the equation $2v^2 = 18$ given $v = 3$. 2. **Recall the formula:** The equation is $2v^2 = 18$. 3. **Substitute the value of $v$:** $$2 \times 3^2 = 18$$ 4. **Calculate the square:** $$2 \times 9 = 18$$ 5. **Multiply:** $$18 = 18$$ 6. **Conclusion:** The equation holds true for $v=3$. Final answer: $18 = 18$ confirms the equation is satisfied.