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Solving and Graphing Inequalities using Multiplication or Division - Problem 1
The rules for solving an equation apply to solving an inequality with one major difference -- anytime you multiply or divide both sides by a negative number, you must change the direction of the inequality sign. When graphing the inequality, keep in mind when to use an open circle versus a closed circle, and which direction the arrow should be pointing.
Working with inequalities is almost exactly like working with equations in how you solve them. There is one huge, huge, huge, huge super important exception though. When you are working with inequalities any time you multiply or divide both sides by a negative value, the direction of the inequality changes.
Let's look at an example: -3x is less than 9. In order to get X all by itself I would want to divide both sides by -3. Since I'm dividing my negative value, this inequality sign needs to change direction. Now I'm going to have x is greater than -3. That's a hugely important piece and you might want to draw a little mark on your paper to remind yourself that that thing changed. It used to look now it looks like that. That's to remind you that you did something on purpose so when you're going back and checking your work you can look for that kind of symbol.
Okay now we just need to graph it. X is now larger than -3. So on my number line I want an open circle because it’s just larger than, it’s not greater than or equal to and I want to mark all values that are greater than -3. This arrow tells me that any number I chose like -2½, +3/4, so whatever, any value I chose that's greater than -3 would be a solution to this inequality.
So before you start doing your homework, make sure, make sure, make sure, please, please, please remember the following thing. Any time you multiply or divide by a negative value the inequality needs to change direction.