domain of 10/ 2x-4 ≤ 0

Solution:
1. Begin with the inequality:
\frac{10}{2x-4} \leq 0

2. Determine where the inequality is undefined. The expression \frac{10}{2x-4} is undefined when the denominator is zero:
2x - 4 = 0
2x = 4
x = 2

So, the expression is undefined at x = 2.

3. Determine where \frac{10}{2x-4} is less than or equal to zero. Since the numerator 10 is positive, for the fraction to be less than or equal to zero, the denominator must be negative or zero.

4. Solve for when the denominator is less than or equal to zero:
2x - 4 \leq 0
2x \leq 4
x \leq 2

5. The inequality \frac{10}{2x-4} cannot equal zero because the numerator (10) is never zero. Therefore, we only need to consider when 2x - 4 < 0.

6. Combine the conditions:
x < 2

Thus, the domain is all real numbers less than 2:
x < 2

7. Express the domain in interval notation:
(-\infty, 2)