Determine the Domain: Analyzing 24/(21x-7)

To determine the domain of the function $\frac{24}{21x-7}$, we need to ensure that the denominator is not equal to zero.

Step 1: Set the denominator equal to zero and solve for $x$:

• $21x - 7 = 0$

• $21x = 7$

• $x = \frac{7}{21}$

• $x = \frac{1}{3}$

The function is undefined when $x = \frac{1}{3}$ because it would cause division by zero.

Step 2: The domain of the function is all real numbers except $x = \frac{1}{3}$.

Therefore, the domain of the function is all $x$ such that $x \neq \frac{1}{3}$.

Thus, the correct answer is $\boxed{ x\ne\frac{1}{3}}$.