algebra 2 8.6

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Solve the equation. Bell Ringer WarmUps –15x + 4 -6 = x

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EXAMPLE 1 Solve a rational equation by cross multiplying Solve: Write original equation. 3(4x + 5) = 9(x + 1) Cross multiply. 12x + 15 = 9x + 9 Distributive property 3x + 15 = 9 Subtract 9x from each side. 3x = – 6 Subtract 15 from each side. x = – 2 Divide each side by 3.

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EXAMPLE 2 Write and use a rational model x is the amount of silver added. 7.5(15 + x) = 100(0.2)(15) Cross multiply. 112.5 + 7.5x = 300 Simplify. 7.5x = 187.5 Subtract 112.5 from each side. x = 25 Divide each side by 7.5.

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GUIDED PRACTICE for Examples 1 and 2 Write original equation. 3(x – 7) = 2(5x ) Cross multiply. 3x – 21 = 10x Distributive property – 7x – 21 = 0 Subtract 10x from each side. – 7x = 21 Subtract 21 from each side. x = – 3 Divide each side by 7. SOLUTION

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GUIDED PRACTICE for Examples 1 and 2 Write original equation. – 4(x – 3) = 5(x + 3) Cross multiply. Distributive property – 9x + 12 = 15 Subtract 5x from each side. Subtract 12 from each side. Divide each side by 9. – 4x + 12 = 5x + 15 – 9x = 3 SOLUTION

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GUIDED PRACTICE for Examples 1 and 2 Write original equation. 1(11x + 8) = x(2x + 5) Cross multiply. Distributive property 2x2 – 6x2 +8 = 0 Subtract 2x2 , and 5 from each side. 11x + 8 = 2x2 + 5x x2 – 3x2 +4= 0 (x – 4)(x + 1) = 0 x = 4 , x = –1

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EXAMPLE 3 Standardized Test Practice SOLUTION Write original equation. Multiply each side by the LCD, 4x. 20 + 7x = –36 Simplify. 7x = – 56 Subtract 20 from each side. x = – 8 Divide each side by 7. )

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EXAMPLE 4 Solve a rational equation with two solutions Solve: Write original equation. Multiply each side by the LCD, x(x–5). x(x –5) – 8x = 3(x – 5) Simplify. x2 – 5x – 8x = 3x – 15 Simplify. x2 – 16x +15 = 0 Write in standard form. (x – 1)(x – 15) = 0 Factor. x = 1 or x = 15 Zero product property The solutions are 1 and 15. Check these in the original equation.

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GUIDED PRACTICE for Examples 3, 4 and 5 Solve the equation by using the LCD. Check for extraneous solutions. 7x + 6 = 6x x = – 6

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GUIDED PRACTICE for Examples 3, 4 and 5 6 + 4x = 6x 6 = 2x x = 3

Homework 8.6 : 

Homework 8.6 Pages: 593 – 595 Exs. 4, 8, 12, 14, 18, 22, 24, 28, 39, 40