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Which values are solutions to the inequality below? Check all that apply.

[tex]\[
\sqrt{x} \geq 9
\][/tex]

A. -81
B. -3
C. 100
D. 3
E. 81
F. 27

Answer :

Sure! Let's solve the inequality [tex]\(\sqrt{x} \geq 9\)[/tex] step by step.

1. Understand the inequality:
- The inequality [tex]\(\sqrt{x} \geq 9\)[/tex] means that the square root of [tex]\(x\)[/tex] should be greater than or equal to 9.

2. Get rid of the square root:
- To eliminate the square root, square both sides of the inequality:
[tex]\[
x \geq 9^2
\][/tex]
- Simplifying the right side gives:
[tex]\[
x \geq 81
\][/tex]

3. Evaluate each option:
- A. [tex]\(-81\)[/tex]: [tex]\(-81\)[/tex] is less than 81, so it is not a solution.
- B. [tex]\(-3\)[/tex]: [tex]\(-3\)[/tex] is less than 81, so it is not a solution.
- C. 100: 100 is greater than 81, so it is a solution.
- D. 3: 3 is less than 81, so it is not a solution.
- E. 81: 81 is equal to 81, so it is a solution.
- F. 27: 27 is less than 81, so it is not a solution.

4. Conclusion:
- The values that satisfy the inequality [tex]\(\sqrt{x} \geq 9\)[/tex] are [tex]\(100\)[/tex] and [tex]\(81\)[/tex].

Therefore, the solutions to the inequality are C. 100 and E. 81.

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