Question

4 solve
7√x + 19 = 24
select the correct choice below and, if necessary, fill in the answer box to complete your choice.
○ a. the solution set is { }. (use a comma to separate answers as needed.)
○ b. the solution set is the empty set.

Explanation:

Step1: Isolate the square root term

Subtract 19 from both sides of the equation \(7\sqrt{x}+19 = 24\).
\(7\sqrt{x}=24 - 19\)
\(7\sqrt{x}=5\)

Step2: Solve for \(\sqrt{x}\)

Divide both sides by 7.
\(\sqrt{x}=\frac{5}{7}\)

Step3: Solve for \(x\)

Square both sides to eliminate the square root.
\(x = (\frac{5}{7})^2=\frac{25}{49}\)

We need to check if this solution is valid by plugging it back into the original equation.
Left - hand side: \(7\sqrt{\frac{25}{49}}+19=7\times\frac{5}{7}+19 = 5 + 19=24\), which is equal to the right - hand side. So \(x=\frac{25}{49}\) is a valid solution.

Answer:

\(\frac{25}{49}\)