31 SOLVING EQUATIONS BY USING ADDITION

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3-1 SOLVING EQUATIONS BY USING ADDITION

• Addition property of equality
• Goal Get x
• Steps
• Add the opposite
• Do the same to both sides of the
• Check

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• D. Examples
• 1. h 8 4
• 2. y (-6) 20
• 3. 4 n 8

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3-2 SOLVING EQUATIONS BY USING SUBTRACTION

• Subtraction property of equality
• Steps (use for addition problems)
• Subtract the number
• Do the same to both sides of the
• Check

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• C. Examples
• x 6 10
• y 14 -5
• m ( -4) 20
• h 6 30

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3-3 SOLVING EQUATIONS BY USING MULTIPLICATION AND
DIVISION

• Properties
• Multiplication property of equality
• Division property of equality
• Steps
• Use inverse operation
• Do the same to both sides of the
• Check
• Examples

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3-4 PROBLEM SOLVING WORKING BACKWARDS

• Problem solving strategies
• 1. 5.
• 2. 6.
• 3. 7.
• 4. 8.
• Example P.109 4

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3-5 SOLVING EQUATIONS USING MORE THAN ONE
OPERATION

• Steps
• Multiply by the denominator (if )
• Add or subtract
• Multiply or divide
• Examples

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3-6 SOLVING EQUATIONS WITH VARIABLES ON BOTH SIDES

• Review simplifying
• 2x 8x
• 2(5c 6)
• 4y 5 y 8
• 2x 3y

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• B. Steps
• Simplify both sides
• a.) distribute
• b.) combine like-terms
• Move variables to one side
• use addition or subtraction
• Use steps for solving

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• C. Examples
• 2(x 3) x 5
• 3c 8c 4 5c 10
• -3(2n 6) ½ (4n 6)
• 2x 1 ½ (4x 2)
• 5(c 4) 5c 8

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3-7 MORE EQUATIONS

• Short cuts
• Fractions multiply by a common denominator
• Decimals multiple by 10, 100, 1000,
• Examples
• x/2 1/3 x/3 ½
• 1.03x 4 -2.15x 8.72

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• C. Solve for x (get x )
• 3x y
• ax b y
• D. Solve for y (get y)
• 2x y 5
• 10x 2y 4