Question

Which one of these inequalities is false? Explain why.

Inequality 1: -5 > x > 10
Inequality 2: -5 > x > -15
Inequality 3: x < -15

Answer 1

Inequality 1, which states '-5 > x > 10', is false because no number can be both greater than 10 and less than -5 simultaneously. Inequalities 2 and 3 are true under the correct conditions for variable x.

Step-by-step explanation:

The question asks which one of the given inequalities is false. After examining each inequality, we find that Inequality 1, which states -5 > x > 10, is false.

This inequality suggests that x is simultaneously greater than 10 and less than -5, which is not possible as these two conditions contradict each other: no number can be both less than -5 and greater than 10 at the same time.

Inequality 2, which is -5 > x > -15, is true because it describes a range where x is less than -5 and greater than -15, which would include any number between those two numbers. Inequality 3, which is x < -15, can also be true if any value of x chosen is less than -15.