Question 7683: 11 - c is greater than or = to 8 --How can I solve this inequality?
Answer by prince_abubu(198)   (Show Source):
You can put this solution on YOUR website! So 11 - c >= 8. Just treat the >= like an equals sign and perform "normal algebra" but watch out! There's a trick here!
OK. At the end, we usually like the variable to be on the left side, and the single number to be on the right. We'll do that. To get the c by itself, we must subtract 11 from both sides first. That gives us:
-c >= -5.
Here's where it gets wacky. There is a rule, and you better know it because it's the one most of us forget. When we multiply an inequality with a negative number on both sides, we FLIP the inequality. We don't like the c to have a negative sign in front of it. After all, we're after c, not -c. So we need to multiply both sides by -1:
c <= 5. <---- multiplying by a negative number flips the sign of the inequality.
For real, why does it happen? That's because the negative side of the number line is a mirror reflection of the positive side. A big number with a negative sign in front of it really is of less value than a small number with a negative sign on it. It's the opposite for positive numbers!
Check out the simple inequality -5 < -1. We agree that -5 is way to the left of -1 on the number line, causing it to be less than -1. When you multiply both sides by -1, you'll end up (for now) with 5 < 1 which is FALSE!. The way to fix that is to flip the inequality from < to >, so now, 5 > 1 which is TRUE!
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