Question

1. solve the equation.

\sqrt{55 - w} - 6 = 2
select the correct choice below and, if necessary, fill in the answer box to complete yo
\bigcirc a. the solution set is \\{\\ \\}.
(simplify your answer. type an integer or a fraction. use a comma to separa
as needed.)
\bigcirc b the solution set is the empty set.

Explanation:

Step1: Isolate the square root term

Add 6 to both sides of the equation $\sqrt{55 - w}-6 = 2$ to get $\sqrt{55 - w}=2 + 6$.
Simplify the right - hand side: $\sqrt{55 - w}=8$.

Step2: Eliminate the square root

Square both sides of the equation $\sqrt{55 - w}=8$. According to the property $(\sqrt{a})^2=a$ (where $a\geq0$), we have $(\sqrt{55 - w})^2 = 8^2$, which simplifies to $55 - w=64$.

Step3: Solve for w

Subtract 55 from both sides of the equation $55 - w=64$: $-w=64 - 55$.
Simplify the right - hand side: $-w = 9$.
Multiply both sides by - 1 to solve for $w$: $w=-9$.

Step4: Check the solution

Substitute $w = - 9$ back into the original equation $\sqrt{55 - w}-6$.
First, calculate $55-(-9)=55 + 9=64$. Then $\sqrt{64}-6=8 - 6 = 2$, which is equal to the right - hand side of the original equation. So $w=-9$ is a valid solution.

Answer:

-9