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2.4 Equations with Variables on Both Sides To solve an equation with variables on both sides, you must use the Addition or Subtraction Properties of Equality to get the variables on the same side of the equation.

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Variables on Both Sides Solve the equation 6x + 3 = 8x – 21. 6x + 3 = 8x – 21 -6x 3 = 2x – 21 +21 + 21 24 = 2x x = 12

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Variables on Both Sides Solve the following equations: a. 2(c – 6) = 9c + 2 2c – 12 = 9c + 2 -2c-2c -12 = 7c + 2 - 2 - 2 - 14 = 7c c = -2 b.7k – 4 = 5k + 16 -5k-5k 2k – 4 = 16 + 4 +4 2k = 20 k = 10

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Identities and Equations with No Solutions An equation has no solution if no value of the variable makes the equation true. –Ex. 2x = 2x + 1 An equation that is true for every value of the variable is an identity. –Ex. 2x = 2x

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Identities and Equations with No Solutions Solve 10 – 8a = 2(5 – 4a). 10 – 8a = 2(5 – 4a) 10 – 8a = 10 – 8a+ 8a 10 = 10 ALWAYS TRUE!!! This equation is true for every value of a, so the equation is an identity.

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Identities and Equations with No Solutions Solve 6m – 5 = 7m + 7 – m. 6m – 5 = 7m + 7 – m 6m – 5 = 6m + 7 - 6m -6m -5 = 7 NOT TRUE!!!! The equation has no solution!

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More Practice!!!! Textbook – p. 98 #4 – 16 even, 22 – 36 even. Homework – worksheet 2.4

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