If 2/(x - 2) = 0, then x =

Rationale

x = 2

The equation \( \frac{2}{x - 2} = 0 \) implies that the numerator must equal zero for the fraction to equal zero. However, since the numerator is a constant (2), it can never be zero, leading to the conclusion that the expression is undefined when \( x = 2 \).

A (1) YOUR ANSWER

If \( x = 1 \), then \( x - 2 = 1 - 2 = -1 \), making the expression \( \frac{2}{-1} = -2 \). This does not equal zero, hence \( x = 1 \) is incorrect.

B (2) CORRECT

When \( x = 2 \), the expression becomes \( \frac{2}{2 - 2} = \frac{2}{0} \), which is undefined. Although this option suggests a solution, it actually indicates a point of discontinuity rather than a valid solution to the equation.

C (4) YOUR ANSWER

If \( x = 4 \), then \( x - 2 = 4 - 2 = 2 \), leading to \( \frac{2}{2} = 1 \). This result does not equal zero, therefore \( x = 4 \) is incorrect.

D (5) YOUR ANSWER

Setting \( x = 5 \) gives \( x - 2 = 5 - 2 = 3 \), resulting in \( \frac{2}{3} \). This expression also does not equal zero, making \( x = 5 \) an incorrect choice.

E (10) YOUR ANSWER

If \( x = 10 \), then \( x - 2 = 10 - 2 = 8 \), leading to \( \frac{2}{8} = \frac{1}{4} \). This value does not equal zero, so \( x = 10 \) is not the solution.

Conclusion

The equation \( \frac{2}{x - 2} = 0 \) cannot be solved as it leads to an undefined situation at \( x = 2 \). None of the provided options yield a valid solution, reinforcing that the equation does not have a solution for any real value of \( x \). The critical takeaway is that the numerator cannot be zero, making the expression undefined when \( x = 2\).

If 2/(x - 2) = 0, then x =

x = 2

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