Video Transcript
Fill in the blank. If 𝑥 is an element of the real numbers, where 𝑥 is greater than the absolute value
of negative one, then 𝑥 is what. Option (A) positive, or is it option (B) negative?
In this question, we are told that a real number 𝑥 is greater than the absolute
value of negative one. We want to use this information to determine if 𝑥 is positive or negative.
To answer this question, we can start by recalling that we say a real number 𝑦 is
positive if it is greater than zero and negative if it is less than zero. We also say that zero itself does not have a sign. We can also recall that the absolute value of a number is the value of the number
without the sign. So the absolute value of negative one is just one. This allows us to rewrite the given inequality as 𝑥 is greater than one, since the
absolute value of negative one is one.
There are then two ways that we can use this to answer the question. First, we can note that one is greater than zero. So 𝑥 must also be greater than zero, showing that 𝑥 must be positive.
We can also show this by considering the possible values of 𝑥 by using a number
line. If 𝑥 is greater than one, then it lies to the right of one on a number line. We can use a hollow circle at one to show that it is not included in this set. We can then compare this set to the set of positive numbers, that is, all of the
numbers to the right of zero on a number line as shown. We can see that every value that satisfies this inequality is to the right of zero,
so it is positive.
Hence, the answer is option (A). If 𝑥 is greater than the absolute value of negative one, then 𝑥 is positive.
