To solve the inequality \( \sqrt{4x + 1} \leq 5.83 \), we first square both sides (since both sides are non-negative):
\[ 4x + 1 \leq (5.83)^2 \]
Calculating \( (5.83)^2 \):
\[ (5.83)^2 = 33.9889 \]
Thus, the inequality becomes:
\[ 4x + 1 \leq 33.9889 \]
Next, we subtract 1 from both sides:
\[ 4x \leq 33.9889 - 1 \] \[ 4x \leq 32.9889 \]
Now, we divide both sides by 4:
\[ x \leq \frac{32.9889}{4} \] \[ x \leq 8.247225 \]
So, the solution to the inequality is:
\[ x \leq 8.247225 \]
Any value for \( x \) that is less than or equal to approximately 8.25 will make the inequality \( \sqrt{4x + 1} \leq 5.83 \) true.