Statement, always, sometimes, or never true for nonzero whole numbers 2x > x2

Question

Statement, always, sometimes, or never true for nonzero whole numbers 2x > x2

Answer 1

The best way to tackle these type of problems is by plugging in numbers and seeing what happens. However, we need to be strategic about the numbers we choose. Since we can choose any nonzero whole number, let us choose a small positive number like 1, a big positive number like 10, a small negative number like -1, and a large negative number like -10. This way we cover all scenarios, which wouldn't be true if we decided to plug in 1, 2, 3, and 4 for example, because in this case we are only considering positive numbers and aren't taking into account the possibility of a negative number. So let's plug in our numbers and see what we get:

The Small Positive Number

2(1) > (1)^2

2 > 1     <-- True

The Large Positive Number

2(10) > 10^2

20 > 100      <-- NOT True

The Small Negative Number

2(-1) > (-1)^2

-2 > 1     <-- NOT True

The Large Negative Number

2(-10) > (-10)^2

-20 > 100     <-- NOT True

So we see that the statement is sometimes true, since one of the results was true and the others weren't. Even more, since we checked every type of number, we know that the statement is only true for small positive numbers.