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:
\[ \boxed{8} \]
1 answer