Which of the following values for x makes the inequality 4x+1−−−−−−√ ≤5.83 true?(1 point) Responses 10 10 9 9 9.5 9.5 8

To solve the inequality \( \sqrt{4x + 1} \leq 5.83 \), we first square both sides to eliminate the square root, which gives us:

\[
4x + 1 \leq (5.83)^2
\]

Calculating \( (5.83)^2 \):

\[
(5.83)^2 = 33.9889
\]

Now we rewrite the inequality:

\[
4x + 1 \leq 33.9889
\]

Next, we subtract 1 from both sides:

\[
4x \leq 32.9889
\]

Now, we divide by 4:

\[
x \leq \frac{32.9889}{4}
\]

Calculating this gives:

\[
x \leq 8.247225
\]

So, the values for \( x \) that satisfy the inequality \( \sqrt{4x + 1} \leq 5.83 \) must be \( x \leq 8.247225 \).

Among the provided options (10, 9, 9.5, 8), the only value that satisfies this inequality is:

\[
\boxed{8}
\]