## Precalculus: Mathematics for Calculus, 7th Edition

$x = \frac{2d-b}{a-2c}$
$Solve$ $the$ $equation$ $for$ $the$ $indicated$ $variable:$ $\frac{ax + b}{cx + d} = 2;$ $for$ $x$ Solve for x Multiply both sides by $cx + d$ $cx+d(\frac{ax + b}{cx + d}) = 2(cx+d)$ Simplify $ax+b = 2cx + 2d$ Subtract 2cx from both sides $ax+b - 2cx = 2cx + 2d - 2cx$ $ax+b - 2cx = 2d$ Subtract b from both sides $ax + b - 2cx - b = 2d - b$ $ax - 2cx = 2d - b$ Factor out $x$ from $ax-2cx$ $x(a-2c) = 2d-b$ Divide both sides by $(a-2c)$ $\frac{x(a-2c)}{a-2c} = \frac{2d-b}{a-2c}$ $x = \frac{2d-b}{a-2c}$