Elementary Algebra

Published by Cengage Learning
ISBN 10: 1285194055
ISBN 13: 978-1-28519-405-9

Chapter 7 - Algebraic Fractions - 7.5 - Fractional Equations and Problem Solving - Problem Set 7.5: 35

Answer

$x = -6$

Work Step by Step

1. Multiply by $x-2$ on both sides of the equation to obtain: $-1 - \frac{5}{x-2} = \frac{3}{x-2}$ $-1(x-2) - 5 = \frac{3(x-2)}{x-2}$ 2. Cancel out $x-2$ in the fraction to simplify: $-1(x-2) - 5 = 3$ 3. Expand and solve for $x$: $-x + 2 - 5 = 3$ $-x + 2 - 5 - 3 = 0$ $-x + 2 -8 = 0$ $-x - 6 = 0$ $-x -6 = 0$ $-x = 6$ $x = -6$
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