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Solving and Graphing Inequalities using Multiplication or Division - Concept

Teacher/Instructor Alissa Fong
Alissa Fong

MA, Stanford University
Teaching in the San Francisco Bay Area

Alissa is currently a teacher in the San Francisco Bay Area and Brightstorm users love her clear, concise explanations of tough concepts

Inequalities follow different rules than equations when dealing with multiplication. Solving inequalities using multiplication involves watching for negative numbers. When we multiply both sides by a negative number we must change the direction of the inequality sign. This happens when using multiplicative inverses to simplify the way we would when solving multi-step equations.

When you're solving Inequalities it's usually like how you would solve an equation when you have an equal sign. However there's one really important difference and and I want to get into that in just a second.
First thing I want you guys to remember when you're asked to graph an inequality on the number line you're going to be using an open circle for one of these symbols or closed circle for one of these symbols.
Then when you're solving you solve it just like it were if it were an equation except if you're multiplying or dividing by a negative number you need to change the direction of the inequality symbol. And I want to show you what I mean and how what that looks like [IB] or why, for example check it out 6 is greater than four. That's a true inequality statement that's always the case this is going to be an example that only uses numbers and no letters so you guys can kind of see like what I'm talking about.
Let's just say I wanted to multiply both sides by -2, and I'm allowed to do that I'm allowed to multiply something by a value as long as I do the exact same process um both sides of the inequality symbol. So I'm multiplying my -2. Now I have a -12 is bigger than -8, that's not true, +12 is bigger than +8. But when this negative gets involved things get really tricky and this is what I'm talking about I'm going to say it like tons and tons of times. If ever you multiply both sides or divide both sides by a negative value you need to change the direction of the inequality symbol. I need to change this guy so instead of saying 12 is greater, excuse me -12 is greater than -8. I need to say -12 is less than -8. You can see that it used to be an inequality sign like this, but I flipped it around there is a little swirly to remind you that now it looks like this. That's the most important thing to keep in mind anytime you're solving inequalities especially if you're going to be multiplying or dividing by a negative value.

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