contestada

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.

Respuesta :

The solution set is [tex]c \geq 5[/tex], meaning that all [tex]c[/tex] at least [tex]5[/tex] satisfy this constraint.

If [tex]c=5[/tex], we have [tex]x < 5[/tex] and [tex]x > 5[/tex], meaning [tex]x[/tex] has to be both greater than and less than [tex]5[/tex], which is impossible.  If [tex]c[/tex] is any greater, [tex]x > c > 5[/tex], so [tex]x[/tex] still must be greater and less than [tex]5[/tex] at the same time.  So for all [tex]c \geq 5[/tex], the system [tex]x < 5, x > c[/tex] has no solution.
driadoll21

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.

         

Otras preguntas