Question

Which of the following values for x makes the inequality 4x+1−−−−−√ ≤5.83 true?(1 point)
Responses

8
8

9.5
9.5

9
9

10

Answer 1

To solve the inequality \( \sqrt{4x + 1} \leq 5.83 \), we will first square both sides to eliminate the square root (keeping in mind this only works because both sides are non-negative):

1. Start with the original inequality:
\[
\sqrt{4x + 1} \leq 5.83
\]

2. Square both sides:
\[
4x + 1 \leq (5.83)^2
\]
\[
4x + 1 \leq 33.9889
\]

3. Subtract 1 from both sides:
\[
4x \leq 32.9889
\]

4. Divide both sides by 4:
\[
x \leq 8.247225
\]

Now, we need to find which of the given options for \( x \) satisfies this inequality:

- \( 8 \) is less than 8.247225 (valid)
- \( 9.5 \) is greater than 8.247225 (invalid)
- \( 9 \) is greater than 8.247225 (invalid)
- \( 10 \) is greater than 8.247225 (invalid)

The only value that makes the inequality true is:
**8**