Question

\\4 = \sqrt{3n + 1}\\

Explanation:

🆕 New Concept Discovered: Solving Radical Equations
Undo the root to isolate the variable.

Step 1: Square both sides

To eliminate the square root on the right side, square both sides of the equation:

$$ (4)^2 = (\sqrt{3n + 1})^2 $$

$$ 16 = 3n + 1 $$

Step 2: Isolate the variable term

Subtract \(1\) from both sides of the equation to isolate the term with \(n\):

$$ 16 - 1 = 3n $$

$$ 15 = 3n $$

Step 3: Solve for n

Divide both sides by \(3\):

$$ n = \frac{15}{3} $$

$$ n = 5 $$

Step 4: Verify the solution

Substitute \(n = 5\) back into the original equation to check:

$$ 4 = \sqrt{3(5) + 1} $$

$$ 4 = \sqrt{15 + 1} $$

$$ 4 = \sqrt{16} $$

$$ 4 = 4 \quad \text{(True)} $$

Answer:

\(n = 5\)