Question: Solve for $v$, where $v$ is a real number.
$$\sqrt[4]{3v + 1} + 3 = 5$$
If there is more than one solution, separate them with commas.
If there is no solution, click on "No solution".
$v =$
1. **State the problem:** Solve for $v$ in the equation $$\sqrt[4]{3v + 1} + 3 = 5$$ where $v$ is a real number.
2. **Isolate the fourth root:** Subtract 3 from both sides:
$$\sqrt[4]{3v + 1} = 5 - 3$$
$$\sqrt[4]{3v + 1} = 2$$
3. **Remove the fourth root by raising both sides to the power of 4:**
$$\left(\sqrt[4]{3v + 1}\right)^4 = 2^4$$
$$3v + 1 = 16$$
4. **Solve for $v$:**
$$3v = 16 - 1$$
$$3v = 15$$
$$v = \frac{15}{3}$$
$$v = 5$$
5. **Check the solution:** Substitute $v=5$ back into the original equation:
$$\sqrt[4]{3(5) + 1} + 3 = \sqrt[4]{15 + 1} + 3 = \sqrt[4]{16} + 3 = 2 + 3 = 5$$
The left side equals the right side, so $v=5$ is a valid solution.
**Final answer:**
$$v = 5$$