Question

Which pair of inequalities would overlap if they were graphed?


x > 0, x < -5
x ≤ 5, x > 5
x ≤ 10, x > 4
x ≥ 10, x ≤ 4

Answer 1

3rd option

Answer 2

The inequalities would overlap if there is a value that satisfies both inequalities at once.

For the first pair, x > 0, x < -5, a number would have to be greater than 0 and less than -5 at the same time. This isn't possible, so it's wrong.

For the second pair, x ≤ 5, x > 5, a value would have to be greater than 5 and less than 5 at the same time, so it's wrong.

For the fourth pair, x ≥ 10, x ≤ 4, a number would have to be greater than 10 and less than 4. Also impossible, so it's wrong.

And that leaves the third option, x ≤ 10, x > 4. There are plenty of values less than 10 but more than 4, such as 5, 7, and 9. So it's our answer.