Question

solve.
\sqrt{x - 11} = 3
select the correct choice below and, if necessary, fill in the answer box to complete your ch
a. the solution(s) is(are) x =
(use a comma to separate answers as needed.)
b. there is no solution.

Explanation:

Step1: Square both sides to eliminate the square root

To solve the equation \(\sqrt{x - 11}=3\), we square both sides of the equation. Squaring the left side \((\sqrt{x - 11})^2\) gives \(x - 11\), and squaring the right side \(3^2\) gives \(9\). So we have the equation:

$$x - 11=9$$

Step2: Solve for x

To isolate \(x\), we add 11 to both sides of the equation \(x - 11 = 9\). Adding 11 to both sides:

$$x-11 + 11=9 + 11$$

Simplifying both sides, we get:

$$x = 20$$

We should also check if this solution is valid by plugging it back into the original equation. Substitute \(x = 20\) into \(\sqrt{x - 11}\):
\(\sqrt{20 - 11}=\sqrt{9}=3\), which matches the right side of the original equation. So \(x = 20\) is a valid solution.

Answer:

A. The solution(s) is(are) \(x = 20\)