As a math tutor, you’ll likely need to sort out a few basics about inequalities.
Generally, people prefer equations to inequalities. Perhaps it’s for the reason that people like one definite answer to a problem: for instance, “x=5”. An inequality gives a set of valid answers, such as “x can be anything less than -1”. I guess we’ll just have to get used to it:)
More problematic – and more fixable – is that many people don’t know which sign is which. We can sort that out right now:
< means less than
> means greater than
10 < 12
20 > 8
Consider the number line:
Both less than and greater than actually refer to placement on the number line. “Less than” means “to the left of”, while “greater than” means “to the right of”. Of course, 10 is greater than 5, which is written 10 > 5. Notice that on the number line, 10 is to the right of 5.
Similarly, 4 is less than 7. In math, you write 4 < 7. Notice that on the number line, 4 is to the left of 7.
It follows, of course, that -10 is less than -5. After all, on the number line, -10 is to the left of -5. Therefore,
-10 < -5
People often have trouble with the idea that -10 < -5. They point out that 10 seems bigger than 5, so why would -10 be less than -5?
The answer is that “less than” doesn’t refer to number size; it means “to the left of”. On a number line, -10 is to the left of -5. Therefore, -10 < -5. Similarly, 5 being to the left of 10, we write 5 < 10.
The practical issues of solving and graphing inequalites will be explored in future posts:)
Jack of Oracle Tutoring by Jack and Diane, Campbell River, BC.