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ALGEBRAIC EQUATIONS

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EQUATIONS AND SOLUTIONS A correct equation is like a balance scale. In order to determine if a given value for a variable is a solution, you can substitute the variable with the possible answer. If the equation is balanced or equal, the answer is a solution.

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SOLVING ADDITION EQUATIONS GOAL: ISOLATE THE VARIABLE Rule #: Always use the INVERSE operation. Rule #2: Whatever you do to the left side you must do to the right side or they are no longer balanced.

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SOLVING To get the variable by itself, take away or subtract the number that was added to the variable. Remember the rule! Because you subtract the number from the side with the variable, you must also subtract the same number from the side without the variable.

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SOLVING SUBTRACTION EQUATIONS GOAL: ISOLATE THE VARIABLE Rule #: Always use the INVERSE operation. Rule #2: Whatever you do to the left side you must do to the right side or they are no longer balanced.

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SOLVING To get the variable by itself, add the number that was subtracted to the variable. Remember the rule! Because you add the number to the side with the variable, you must also add the same number from the side without the variable.

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SOLVING MULTIPLICATION EQUATIONS GOAL: ISOLATE THE VARIABLE Rule #: Always use the INVERSE operation. Rule #2: Whatever you do to the left side you must do to the right side or they are no longer balanced.

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SOLVING To get the variable by itself, divide the number that was multiplied to the variable. Remember the rule! Because you divide the number on the side with the variable, you must also divide the same number from the side without the variable.

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SOLVING DIVISION EQUATIONS GOAL: ISOLATE THE VARIABLE Rule #: Always use the INVERSE operation. Rule #2: Whatever you do to the left side you must do to the right side or they are no longer balanced.

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SOLVING To get the variable by itself, multiply the number that is the divisor. Remember the rule! Because you multiply the number on the side with the variable, you must also multiply by the same number on the side without the variable.

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GOAL: ISOLATE THE VARIABLE Rule 1: Always use the inverse operation. Rule 2: Whatever you do to the left side you must do to the right side or they are no longer balanced. Fill in on pages 8 AND 9! SOLVING: 1.Combine all like terms, if necessary. 2.If there are variables on both sides, get the variables on one side by using the opposite operation to get rid of the variable with the smallest coefficient. 3.Use opposite or inverse operations to get rid of the numbers on the same side as the variable. 4.Don’t forget – Whatever you do to one side, you must do the other.

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DECIMALS- PAGE 8 7.4 + y = 18. 2 -7.4 - 7.4 y= 10.8 2.3z= 9.2 2.3 z= 4

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FRACTIONS- PAGE 9 h + 3/8 = 5/8 - 3/8 -3/8 h = 2/8 (1/4) 1/2n=3/8 1/2 n= 6/8 (3/4)

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