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Answer :
To solve the inequality [tex]\(\sqrt{x} \geq 9\)[/tex], we need to find the values of [tex]\(x\)[/tex] that satisfy this condition.
Here’s how you can solve it step-by-step:
1. Understand the Inequality: The inequality is [tex]\(\sqrt{x} \geq 9\)[/tex]. This means the square root of [tex]\(x\)[/tex] must be greater than or equal to 9.
2. Remove the Square Root: To eliminate the square root, square both sides of the inequality. This gives us:
[tex]\[
x \geq 9^2
\][/tex]
3. Calculate the Square: Compute [tex]\(9^2\)[/tex], which is 81. Thus, we have:
[tex]\[
x \geq 81
\][/tex]
4. Determine Solutions: Now, any value of [tex]\(x\)[/tex] that is equal to or greater than 81 will satisfy the inequality.
Let's check each of the given options to see which ones are solutions:
- A. 81: Since 81 is equal to 81, it satisfies [tex]\(x \geq 81\)[/tex].
- B. 27: 27 is less than 81, so it does not satisfy the inequality.
- C. -3: -3 is less than 81, so it does not satisfy the inequality.
- D. 3: 3 is less than 81, so it does not satisfy the inequality.
- E. 100: 100 is greater than 81, so it satisfies the inequality.
- F. -81: -81 is less than 81, so it does not satisfy the inequality.
After checking all the options, the solutions to the inequality [tex]\(\sqrt{x} \geq 9\)[/tex] are:
- A. 81
- E. 100
Here’s how you can solve it step-by-step:
1. Understand the Inequality: The inequality is [tex]\(\sqrt{x} \geq 9\)[/tex]. This means the square root of [tex]\(x\)[/tex] must be greater than or equal to 9.
2. Remove the Square Root: To eliminate the square root, square both sides of the inequality. This gives us:
[tex]\[
x \geq 9^2
\][/tex]
3. Calculate the Square: Compute [tex]\(9^2\)[/tex], which is 81. Thus, we have:
[tex]\[
x \geq 81
\][/tex]
4. Determine Solutions: Now, any value of [tex]\(x\)[/tex] that is equal to or greater than 81 will satisfy the inequality.
Let's check each of the given options to see which ones are solutions:
- A. 81: Since 81 is equal to 81, it satisfies [tex]\(x \geq 81\)[/tex].
- B. 27: 27 is less than 81, so it does not satisfy the inequality.
- C. -3: -3 is less than 81, so it does not satisfy the inequality.
- D. 3: 3 is less than 81, so it does not satisfy the inequality.
- E. 100: 100 is greater than 81, so it satisfies the inequality.
- F. -81: -81 is less than 81, so it does not satisfy the inequality.
After checking all the options, the solutions to the inequality [tex]\(\sqrt{x} \geq 9\)[/tex] are:
- A. 81
- E. 100
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