Question

2.) \sqrt{3x + 4} = 5

Explanation:

Step1: Square both sides to eliminate square root

To solve the equation \(\sqrt{3x + 4}=5\), we square both sides of the equation. Squaring the left side \((\sqrt{3x + 4})^2\) will give us \(3x + 4\), and squaring the right side \(5^2 = 25\). So we get the equation:
\(3x + 4=25\)

Step2: Solve for x

Subtract 4 from both sides of the equation \(3x + 4 - 4=25 - 4\), which simplifies to \(3x = 21\). Then divide both sides by 3: \(\frac{3x}{3}=\frac{21}{3}\), so \(x = 7\).

Step3: Check the solution

Substitute \(x = 7\) back into the original equation \(\sqrt{3(7)+4}=\sqrt{21 + 4}=\sqrt{25}=5\), which matches the right side of the original equation. So the solution is valid.

Answer:

\(x = 7\)