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

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.

Answer 2

c = 6

Explanation:

The compound inequality is c < x < 5

If we want a value of c such that there are no solutions, we need to make that inequality false.

From the inequality we can see that 5 must be greater than c to be true.

Therefore, we need to choose a value smaller or equal than 5.

For example, c=6.

If c = 6, that means that x is greater than 6 and smaller than 5. That's impossible, there is no number that meets that.

Therefore, our compound inequality 6 < x < 5 has no solutions.