Find the Domain: Understanding 8/(x - 2.5)

To determine the domain of the function $\frac{8}{x - 2\frac{1}{2}}$, we'll follow these steps:

• Step 1: Identify where the denominator is zero.

• Step 2: Solve for $x$ in this scenario to find exclusions from the domain.

• Step 3: Provide the domain, excluding these $x$ values.

Let's go through the problem step by step:
Step 1: We note that the function is undefined where the denominator equals zero.
Thus, set the denominator equal to zero: $\begin{aligned} x - 2\frac{1}{2} &= 0 \end{aligned}$
Step 2: Solve for $x$: $\begin{aligned} x &= 2\frac{1}{2} \end{aligned}$
Step 3: The domain of the function is all real numbers except $2\frac{1}{2}$.
Therefore, we express the domain as all real numbers $x$ such that $x \ne 2\frac{1}{2}$.

Thus, the solution to the problem is $x \ne 2\frac{1}{2}$.