In this image, we are given a right-angled triangle where one of the angles is $31^\circ$, and the side adjacent to this angle is labeled $4x - 1$. We are asked to find the value of $x$.

To solve this, we can use trigonometric functions. Specifically, the cosine function is appropriate since it relates the adjacent side to the hypotenuse:

$\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}$

Here, $\theta = 31^\circ$, the adjacent side is $4x - 1$, and the hypotenuse is not labeled. However, based on the choices given, we likely need to compare the calculated adjacent side to possible values of $x$. Could you confirm if any additional side information is provided elsewhere, or should we proceed with more assumptions?