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

The solution set is
`c \geq 5`, meaning that all
`c` at least
`5` satisfy this constraint.

If
`c=5`, we have
`x < 5` and
`x > 5`, meaning
`x` has to be both greater than and less than
`5`, which is impossible. If
`c` is any greater,
`x > c > 5`, so
`x` still must be greater and less than
`5` at the same time. So for all
`c \geq 5`, the system
`x < 5, x > c` has no solution.