\( 1 \leftarrow \quad \) Solve. Check your solution. \[ \begin{array}{l}-\frac{24}{29}=x+\frac{1}{29} \\ x=\square \text { (Type an integer or a fraction.) }\end{array} \]

To solve the equation \(-\frac{24}{29} = x + \frac{1}{29}\), we first isolate \(x\) by subtracting \(\frac{1}{29}\) from both sides: \[ x = -\frac{24}{29} - \frac{1}{29} = -\frac{24 + 1}{29} = -\frac{25}{29} \] Thus, the solution is: \(x = -\frac{25}{29}\). Now, let's check the solution by plugging it back into the original equation: \[ -\frac{24}{29} = -\frac{25}{29} + \frac{1}{29} \] Calculating the right side: \[ -\frac{25}{29} + \frac{1}{29} = -\frac{25 - 1}{29} = -\frac{24}{29} \] Since both sides are equal, our solution \(x = -\frac{25}{29}\) is verified.