Lesson 6-2 : HOW TO SOLVE INEQUALITIES BY MULTIPLICATION AND DIVISION
INTRODUCTION!!!!!!:
You may think all math is hard. You might faint at the sight or mention of the word Algebra. If so, this is the lesson/study guide for YOU. I understood it, so anyone can. It is called "Solving Inequalities by Multiplication and Division." Do you know how to multiply? How to divide? Well, if so, to learn this lesson, all you must do is follow the step-by-step directions of the examples. Ready, set, ALGEBRA!!!!!! :) *************KEEP IN MIND, THE SIGNS "EQUAL TO OR LESS THAN" AND "EQUAL TO OR GREATER THAN" CANNOT BE USED ON THIS COMPUTER. THEY WILL APPEAR LIKE SO: equal to or less than: <_ equal to or greater than: >_ THANK YOU!!!!
Vocabulary:
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Multiplication Property of Inequalities-If each side of an inequality is multiplied by a negative number,the direction of the inequality symbol changes. These examples illustrate Multiplication Property of Inequalities.
Examples:
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Example 1:
say you have an inequality, like... this one: 8 ( n + 2 ) < 4n + 3. How are you supposed to work it out? It looks pretty nasty, huh? :) Well, just watch and see.
Start out doing the Distributive property- 8 (n + 2 ) < 4n + 3
Tada!!! 8n + 2 < 4n + 3
Next, combine like terms, like the "4n" and "8n" -4n -4n
Once again, TADA!! 4n + 2 < 3
See how nice that looks? Keep combining!!! -2 -2
And now we end up with... 4n 1
Now comes the easy part... divide each side by 4. /4 /4
Now you end up with a nice looking... n < 0.25 OR n < 1/4
Example 2
6Y< 12
3
First multiply each side by -3.
6Y< 12x-3
-3x-3
to get...
6Y>-36 (remember to flip the inequality when multiplying or dividing by a negative)
Now divide by 6 on both sides
Y>-6
Now Your Done!
Example 3
Negative four times a number is less than or equal to negative twenty-four.
-4N< -24
Divide by -4 to get...
N>6
Key Concepts Multiplying by a Positive Number
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If each side of a true inequality is multiplied by the same positive number,the resulting inequality is also true.
SYMBOLS:
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If a and b are any numbers and c is a positive number, the following are true: a>b then ac>bc,and if a<b,then ac<bc
Multiplying by a Negative Number
WORDS:
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IF each side of a true inequality is multiplies by the same negative number, the direction of the inequality symbol must be reversed so that the resulting inequality is also true. (aka: if you multiply by a negative number on both sides, then you have you flip the direction of the sign.)
Symbols:
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If a and b are any numbers and c is a negative number,the following are true. If a>b,then ac<bc,and if a<b,then ac>bc
Additional Information:
Online resources:
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AV MH AR ZM