Question

If x<5 and x>c, give a value of c such that there are no solutions to the compound inequality. Explain why there are no solutions.

Answer 1

Answer: The value of c could be 5 or any number greater than 5.

The solution is the intersection of both solution sets of the given inequalities.

The solutions of the compound inequality must be solutions of both inequalities.

A number cannot be both less than 5 and greater than 5 at the same time.

Explanation:

Answer 2

c = 5 is a solution for c.

Explanation:

If x < 5 and x > c, then we have to find the value c such that the compound inequality will have no solution.

Now, let us assume c = 5, then the inequality becomes x < 5 and x > 5. and hence, the compound inequality will have no solution.

Because if we choose x = 4 which is less than 5 but it is not greater than 5 from the second condition.

Therefore, c = 5 is a solution for c. (Answer)