### Algebraic Equations: Solving Square Root Equations#### Problem 1: Solving for xConsider the following algebraic equation involving square roots:\[ \frac{\sqrt{x}}{3x - 5} = \frac{6}{\sqrt{x}} \]**Question:**What is the value of \( x \) when this equation is satisfied?#### Multiple Choice Answers:- A) \( \frac{15}{8} \)- B) \( \frac{5}{17} \)- C) \( \frac{30}{17} \)- D) \( \frac{11}{3} \)To solve this problem, follow these steps:1. **Isolate the square roots:** Multiply both sides by \( \sqrt{x}(3x - 5) \) to eliminate the fractions.2. **Simplify the equation:** Combine like terms and solve for \( x \).3. **Verify the solution:** Ensure the solution satisfies the original equation by substituting \( x \) back into the equation.Choose the correct answer from the given options. **Solution Steps:**1. Start by cross-multiplying to get rid of the fractions:\[ \sqrt{x} \cdot \sqrt{x} = 6 \cdot (3x - 5) \]2. We know that \(\sqrt{x} \cdot \sqrt{x} = x\), so:\[ x = 6(3x - 5) \]3. Distribute the 6:\[ x = 18x - 30 \]4. Move all terms involving \( x \) to one side of the equation:\[ x - 18x = -30 \]\[ -17x = -30 \]5. Divide both sides by -17:\[ x = \frac{30}{17} \]Thus, the value of \( x \) is \(\frac{30}{17}\).Therefore, the correct answer is:- C) \( \frac{30}{17} \)

Name: ### Algebraic Equations: Solving Square Root Equations#### Problem 1:
Uploaded: 2024-03-20T07:06:41.000Z
Channel: Bartleby
Description: ### Algebraic Equations: Solving Square Root Equations#### Problem 1: Solving for xConsider the following algebraic equation involving square roots:\[ \frac{\sqrt{x}}{3x - 5} = \frac{6}{\sqrt{x}} \]**Question:**What is the value of \( x \) when this