Question

Solve. x/x-19 ≥ 0

Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

A. The solution set is x. (Use at least one inequality or compound inequality to express your answer. For answers with more than one inequality, separate the inequalities by a comma or the word 'or.)

B. The solution is all real numbers

C. There is no solution.

Answer 1

To solve the inequality x/(x-19) ≥ 0, consider the cases when x and (x-19) have the same sign. The solution set is 0 ≤ x < 19 (choice A). Therefore correct option is A

Step-by-step explanation:

To solve the inequality x/(x-19) ≥ 0, we need to find the values of x that make the inequality true. A fraction is positive when the numerator and denominator have the same sign.

So, let's consider the cases where both x and (x-19) are either positive or negative.

Case 1: x and (x-19) are both positive:

If x is greater than 19, then (x-19) will also be positive. So, the solution for this case is x > 19.

Case 2: x and (x-19) are both negative:

If x is less than 19, then (x-19) will also be negative. So, the solution for this case is x < 19.

Combining both cases, the solution set is x.

Therefore, the correct choice is A: The solution set is x.