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MATH 1050 SECTION 2 QUIZ 2 FALL 2009 1. 8 points. Find all solutions of the equation 2 1 2 = + . (x − 4)(x − 2) (x − 4) (x − 2) solution. First, we eliminate the denominators. Multiplying by (x − 4) gives: 2 2(x − 4) =1+ . (x − 2) (x − 2) We then multiply by (x − 2): 2 = (x − 2) + 2(x − 4) 2 = 3x − 10 3x = 12 x=4 Plugging this solution into the original equation gives division by zero, so the equation has no solutions. In the next two questions, solve the inequalities and graph solutions on the real number line: 2. 6 points. |x − 5| < −1. solution. As an absolute value, the quantity on the left of the inequality is always nonnegative and so cannot be less than a negative number. Thus, this inequality has no solutions. x − 3 ≥ 4. 3. 6 points. 2 x−3 x−3 ≥ 4 and ≤ −4. We solve these separately. 2 2 x−3 ≥ 4. 2 x − 3 ≥ 8. x ≥ 11. solution. This inequality splits into two parts: Now the second part: x−3 ≤ −4. 2 x − 3 ≤ −8. x ≤ −5. 1