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## Algebra basics

### Course: Algebra basics>Unit 3

Lesson 6: Multi-step inequalities

# Multi-step inequalities

Sal solves several multi-step linear inequalities. Created by Sal Khan.

## Want to join the conversation?

• At , Sal says that you swap the inequality sign when you divide by a negative number. But I'm pretty sure my teacher taught me that when you divide by a negative, you would change > to a less than OR EQUAL TO symbol, not just to a <. So confused...who is right.... •   I am sorry, but your Math teacher must have misspoke. When solving inequalities, like, say, this one:

-2x+5<25

You would cancel out the +5 with -5 and subtract 25 by 5, so you're left with this:

-2x<20.

But now, since you're dividing by -2 (remember that multiplying or dividing by a negative number will reverse the sign) it will no longer be less than, it will be greater than:

-2x/-2>20/-2

x>-10.

So, therefore, you cannot go from < or > to an "or equal to" sign just by dividing or multiplying by a negative number.

Behold. Math.

Hope this helps :D
• Why does Sal write a negative infinity sign? I don't get what it means. •  Number lines continue forever in 2 directions. We use positive infinity for the rigth side and -infinity for the left side. There is no larger numbers and there is no smallest number. The line extends forever.

Hope that helps,
• Is there a clever way to remember to change the direction of the sign when dividing or multiplying by a negative number? •  Think of the negative sign as a bad thing, or losing something.
Think of the positive sign as a good thing, or gaining something.
( - )( + ) = losing something good = negative
( - )( - ) = losing something bad = positive
( + )( + ) = gaining something good = positive
( + )( - ) = gaining something bad = negative
Did that help?

• How would you do it if you had to go backwards (You were given the solution and asked to find the inequality that has that solution)? • Just like in simple math. If I said " add two numbers together that equal six
2+4=6, and we are done. as Sal likes to say. So ... ..
Pic a number -1 make an expression where X = -1
4x+3<-1. You see it worked and just like the addition there are only a couple of possibilities compared to all the possibilities that could work. Just check your work!
• To whom it may concern,
I hope you and your family is safe especially during this tough pandemic! • when would you need to know inequalities? • It is helpful to know inequalities in the future: say you are baking something, for example a cake, and you can't remember how much sugar you needed. You knew that it was more than how much flour you needed, multiplied by two. This could be expressed as S< 2F.
You may not see inequalities pop out at you as: "Oh. That's an inequality!", but they are there. They are there everyday. It could be in homework or cooking or practically anything, but they are there. :)
• How would you solve an inequality that contains exponents?
Thanks very much! • Does anyone else use the alligator mnemonic
device?:
The alligator eats the larger number.

And if you don't share your method.

It may help many people. • Am I the only one watching the videos for College Algebra and being bored? Like for the past 3 videos I have just been doodling on a paper. • doesn't the negative and a negative equal to a positive number? • 