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Question 9 of 30

Enter the solution to the inequality below. Enter your answer as an inequality. Use [tex]$=\ \textless \ $[/tex] for [tex]$\leq$[/tex] and [tex]$\ \textgreater \ =$[/tex] for [tex]$\geq$[/tex]. For example, [tex]$-1 \leq x \leq 1$[/tex] can be written as [tex]$-1=\ \textless \ x=\ \textless \ 1$[/tex].

[tex]\[
\sqrt{x} \leq 11
\][/tex]

Answer here:



Answer :

GinnyAnswer
To solve the inequality [tex]\(\sqrt{x} \leq 11\)[/tex], we follow these steps:

1. Understand the inequality:
[tex]\[\sqrt{x} \leq 11\][/tex]

2. Square both sides to eliminate the square root:
[tex]\[(\sqrt{x})^2 \leq 11^2\][/tex]
Simplifies to:
[tex]\[x \leq 121\][/tex]

Note that squaring both sides is a valid operation because the square function is monotonic (non-decreasing) on the domain of [tex]\(\sqrt{x}\)[/tex], which is [tex]\(x \geq 0\)[/tex].

3. Determine the domain:
Since the square root function is defined when the input is non-negative, we have an additional constraint:
[tex]\[x \geq 0\][/tex]

4. Combine both constraints:
The combined solution set is:
[tex]\[0 \leq x \leq 121\][/tex]

5. Express the solution in the required format:
[tex]\[0 =< x \leq 121\][/tex]

So, the final answer is:
[tex]\[0 =< x =< 121\][/tex]