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Notes 2.4– Solving Equations with Variables on Both Sides

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I. Procedure: ELIMINATE Fractions!!! How:MULTIPLY the whole equation by the LCD. Ex. -

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2.) SIMPLIFY BOTH sides of the equation. How: Distribute first!! (If needed) then COMBINE like terms on each side of the EQUATION. Ex. -

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3.) Get all VARIABLE terms on the SAME SIDE of the equation. How: Choose the variable term on ONE side and add the OPPOSITE of that term to BOTH sides. Ex. -

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4.) Get all CONSTANT terms on the OPPOSITE SIDE of the equation. How: Choose the CONSTANT on the SAME side of the variable term and add the OPPOSITE to BOTH sides. Ex. -

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5.) SOLVE THE EQUATION for the variable. How: DIVIDE (or multiply) BOTH sides of the equation by the COEFFICIENT of the variable. Ex. -

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Solve the following equations: 1) 2) II. Examples

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3) 4)

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III. Identities and No Solution: Definition: An IDENTITY is and equation that is TRUE for every possible value of the variable. Solve the following equation Ex. -

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An equation that has NO SOULTION if there is no value for the variable that makes the equation TRUE. Solve the following equation Ex. -

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Homework : Section 2.4pages 114-116 #’s 6-8, 10-22 even, 30-34 even, 39

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