Question

1. solve the equation.

\sqrt{27 - w} - 5 = 1
select the correct choice below and, if necessary, fill in the answer box to complete your choice.
\bigcirc a. the solution set is \\{ \\ \\}.
(simplify your answer. type an integer or a fraction. use a comma to separate answers as needed.)
\bigcirc b. the solution set is the empty set.

Explanation:

Step1: Isolate the square root term

Add 5 to both sides of the equation \(\sqrt{27 - w}-5 = 1\) to get \(\sqrt{27 - w}=1 + 5\).
Simplifying the right side, we have \(\sqrt{27 - w}=6\).

Step2: Eliminate the square root

Square both sides of the equation \(\sqrt{27 - w}=6\) to obtain \(27 - w=6^{2}\).
Calculating \(6^{2}\), we get \(27 - w = 36\).

Step3: Solve for \(w\)

Subtract 27 from both sides: \(-w=36 - 27\).
Simplifying the right side gives \(-w = 9\).
Multiply both sides by - 1: \(w=-9\).

Step4: Check the solution

Substitute \(w = - 9\) back into the original equation: \(\sqrt{27-(-9)}-5=\sqrt{36}-5 = 6 - 5=1\), which is equal to the right - hand side of the original equation. So \(w=-9\) is a valid solution.

Answer:

A. The solution set is \(\{-9\}\)