Question

find the real solutions of the equation.
\sqrt{3x - 5} = 7
what is the solution set? select the correct choice below and fill
a. \\{ \\}
(simplify your answer. use a comma to separate answer
b. there are no real solutions.

Explanation:

Step1: Square both sides to eliminate square root

To solve the equation \(\sqrt{3x - 5}=7\), we square both sides of the equation. Squaring the left side \((\sqrt{3x - 5})^2\) gives \(3x - 5\), and squaring the right side \(7^2\) gives \(49\). So we get the equation \(3x - 5 = 49\).

Step2: Solve for x

First, add 5 to both sides of the equation \(3x - 5 = 49\). Adding 5 to both sides, we have \(3x-5 + 5=49 + 5\), which simplifies to \(3x=54\). Then, divide both sides by 3: \(\frac{3x}{3}=\frac{54}{3}\), so \(x = 18\).

Step3: Check the solution

We need to check if \(x = 18\) satisfies the original equation. Substitute \(x = 18\) into the left side of the original equation: \(\sqrt{3(18)-5}=\sqrt{54 - 5}=\sqrt{49}=7\), which is equal to the right side of the original equation. So \(x = 18\) is a valid solution.

Answer:

A. \(\{18\}\)