𝑥 is an integer. Which of the following statements is true? Circle your answer. Four 𝑥 is always even. Four 𝑥 is always odd. Or four 𝑥 could be odd or even.
We’re told that 𝑥 is an integer. We remember that an integer is a number with no fractional parts. It will be positive or negative whole numbers, sometimes called counting numbers. And we’re trying to consider what happens if we multiply this integer by four. We know that four is even. If we multiply four by 𝑥, where 𝑥 is an integer, then four 𝑥 will be a multiple of four.
Let’s consider some multiples of four. Four times one is four. Four times two is eight. Four times three is 12. Four times four is 16. We should notice that these multiples of four are all even. More generally, we can say that an odd number multiplied by an even number equals an even number. And even numbers multiplied by even numbers will also be even.
Since we’re multiplying whatever our integer is by four and four is an even number, the outcome will always be even.