Not All Equations Are Created Equal
You might encounter a few equations on the HiSet that, instead of having an =, the equation has an inequality: <, >, ≤, ≥ . If you are unfamiliar with these symbols, visit the ratios and proportions page and scroll down to Other Comparisons.
The good news is they are worked just like equations with equal signs. Of course, there is always an exception. The not so good news is when you divide by a negative number, you have to flip the inequality. See? That doesn’t even qualify as bad news.
It’s Example Time!
Remember solve like you would an equation that has an equal sign.
What does b > 1 mean? It means that we don’t know what b’s value actually is, but it certainly is greater than 1. If we plugged 1 back into the equation, then both sides would be equal, which makes the inequality false. If we plugged a number less than 1 into the equation, then it would also be false. For the left side to remain greater than the right side, b must be greater than 1.
Now with a Negative Number…
We have b is less than -1, not greater than. Do you see why? If you plug -1 back into the original equation, you would get -15(-1) + 6 > 21, which is not true because 21 is not greater than 21; it is equal. If you plug a number greater than -1, then it would also be false. Let’s use 1 for example: -15(1) + 6 works out to be -15 + 6 = -9. -9 is less than 21; therefore, b < -1.
Another way to look at it is, you know that b will also have to be a negative number so that when it is multiplied by -15, it will turn into a positive number. Any positive number greater than 15 plus 6 will be greater than 21. Therefore, it makes sense that in order to have -15b + 6 > 21, you have to have b < -1.