Algebra Period 4

The Multiplication Property of Inequality 4-3
Solving Inequalities  with multiplication or division:
Again, you will use your equation skills, but this time with the Multiplicative Inverse Property.

ONE MAJOR DIFFERENCE FROM EQUATIONS;

When you multiply or divide by a NEGATIVE to BALANCE, you must SWITCH the inequality SYMBOL! 

(REMEMBER --->Does not apply to adding or subtracting negatives.)


EXAMPLE: -3y > 9

You need to divide both sides by NEGATIVE 3 so the symbol will switch from > to < in the solution y < -3 is the answer

If you want to understand why:

3 < 10

Now multiply both sides by -1 (mult prop of equality)

You get -3 < -10, but THAT'S NOT TRUE!!!

You have to SWITCH THE SYMBOL to make the answer true: -3 > -10


REMEMBER: when you MULTIPLY or DIVIDE by a NEGATIVE, the symbol SWITCHES



Using the Properties Together 4-4


Same as equations except make sure you switch the symbol if you multiply or divide by a negative!

Always finish with the variable on the left-- makes it so much easier to graph

Check with whatever solution is easiest in the solution set!

Somethings to remember with two step inequalities:

Before you start, you may want to clear fractions or decimals, but if you don't mind using them, just get started with the checklist below.
If you want to clear them, you should do that right after you distribute (between steps 1 and 2 below)

1. Do distributive property first (if necessary)

2 Combine like terms on each side of the wall (equal sign)

3. Jump the variables to one side of the wall (get all the variables on one side of the equation) by using the Additive Inverse Property (add or subtract using the opposite sign of the variable term)

4. Add or subtract

5. Multiply or divide

6. Make sure the variable is on the LEFT side when finished.