To solve the inequality \( \sqrt{4x + 1} \leq 5.83 \), we first square both sides to eliminate the square root:
\[ 4x + 1 \leq (5.83)^2 \]
Calculating \( (5.83)^2 \):
\[ (5.83)^2 = 33.9889 \]
Now, we can rewrite the inequality:
\[ 4x + 1 \leq 33.9889 \]
Next, we'll isolate \( x \):
- Subtract 1 from both sides:
\[ 4x \leq 33.9889 - 1 \] \[ 4x \leq 32.9889 \]
- Divide both sides by 4:
\[ x \leq \frac{32.9889}{4} \] \[ x \leq 8.247225 \]
Now we compare this result with the given options: 8, 9, 9.5, and 10.
The possible values for \( x \) that satisfy \( x \leq 8.247225 \) include:
- 8 (this value is valid)
- 9 (this value is not valid)
- 9.5 (this value is not valid)
- 10 (this value is not valid)
Thus, the only value from the options that makes the inequality \( \sqrt{4x + 1} \leq 5.83 \) true is 8.
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