To find the x-intercept of an equation, we set $y = 0$ and solve for $x$. Given the equation:

$y - 1 = \frac{1}{4x + 1}$

Step 1: Set $y = 0$

$0 - 1 = \frac{1}{4x + 1}$ This simplifies to: $-1 = \frac{1}{4x + 1}$

Step 2: Solve for $x$

Multiply both sides by $4x + 1$ to eliminate the denominator: $-1 \cdot (4x + 1) = 1$ $-(4x + 1) = 1$ $-4x - 1 = 1$

Add 1 to both sides: $-4x = 2$

Now, divide by -4: $x = -\frac{1}{2}$

Thus, the x-intercept is $x = -\frac{1}{2}$.

Would you like further details or have any questions?

Here are 5 related questions for further practice:

1. What is the y-intercept of the equation $y - 1 = \frac{1}{4x + 1}$?
2. How do you find the slope of this equation?
3. What happens to the x-intercept if the equation is multiplied by a constant?
4. How do you determine if the graph of this equation is linear or nonlinear?
5. What is the domain and range of this equation?

Tip: Always double-check that the equation is in a solvable form before finding intercepts!