Math Algebra Worksheet 2 Key

ALGEBRA II CP 8.6 WORKSHEET Solve the following equations. Be sure to check for extraneous solutions. 1. (5x - 7)/(2x - 1) = 10x (5x - 7) = 10x(2x - 1) 5x - 7 = 20x² - 10x 0 = 20x² - 15x + 7 0 = (4x - 1)(5x - 7) 4x - 1 = 0 or 5x - 7 = 0 x = 1/4 or x = 7/5 Extraneous Solution: YES or NO Answer: x = 1/4, 7/5 2. x/(x + 8) = (x + 8)/(x + 5) x(x + 5) = (x + 8)(x + 8) x² + 5x = x² + 16x + 64 0 = 11x + 64 x = -64/11 Extraneous Solution: YES or NO Answer: x = -64/11 3. x + 2/x = 3 - 2/x x(x + 2/x) = x(3 - 2/x) x² + 2 = 3x - 2 x² - 3x + 4 = 0 LCD: 2x Extraneous Solution: YES or NO Answer: No Solution 4. 5x - 7/x = 10 + 2/x x(5x - 7/x) = x(10 + 2/x) 5x² - 7 = 10x + 2 5x² - 10x - 9 = 0 (5x + 3)(x - 3) = 0 5x + 3 = 0 or x - 3 = 0 x = -3/5 or x = 3 LCD: x Extraneous Solution: YES or NO Answer: x = -3/5, 3 5. 3/(2x - 1) + 4/(x + 1) = 2/(2x - 1) (2x - 1)(3/(2x - 1) + 4/(x + 1)) = (2x - 1)(2/(2x - 1)) 3(x + 1) + 4(2x - 1) = 2(x + 1) 3x + 3 + 8x - 4 = 2x + 2 9x - 1 = 2x + 2 7x = 3 x = 3/7 LCD: 2(x - 1) Extraneous Solution: YES or NO Answer: x = 3/7 6. 3/(x + 1) + 5/(2x) = 3/(2x) 2x(x + 1)(3/(x + 1) + 5/(2x)) = 2x(x + 1)(3/(2x)) 6x + 5(x + 1) = 3(x + 1) 6x + 5x + 5 = 3x + 3 8x + 5 = 3x + 3 5x = -2 x = -2/5 LCD: 2x(x + 1) Extraneous Solution: YES or NO Answer: x = -2/5 8. 6/(x+1) + 2/(x+6) = 1 (x+1)(x+6)(6/(x+1) + 2/(x+6)) = (x+1)(x+6)(1) 6(x+6) + 2(x+1) = (x+1)(x+6) 6x + 36 + 2x + 2 = x² + 7x + 6 x² + 7x + 6 = 8x + 38 x² - x - 32 = 0 (x-8)(x+4) = 0 x = 8, -4 LCD: (x+1)(x+6) Extraneous Solution: YES or NO Answer: 8, -4 9. 8/(x-3) + 5/(x+5) = x/(x²-2x-15) (x-3)(x+5)(8/(x-3) + 5/(x+5)) = (x-3)(x+5)(x/(x²-2x-15)) 8(x+5) + 5(x-3) = x 8x + 40 + 5x - 15 = x 12x + 25 = x 11x = -25 x = -25/11 LCD: (x-3)(x+5) Extraneous Solution: YES or NO Answer: -25/11 10. 3/(x+1) + 12/(x²+2x+1) = 2/(x+1) (x+1)²(3/(x+1) + 12/(x²+2x+1)) = (x+1)²(2/(x+1)) 3(x+1) + 12 = 2(x+1) 3x + 3 + 12 = 2x + 2 x + 13 = 2x + 2 x = 11 LCD: (x+1)² Extraneous Solution: YES or NO Answer: 11