Answer
$x = \frac{2d-b}{a-2c}$
Work Step by Step
$Solve$ $the$ $equation$ $for$ $the$ $indicated$ $variable:$
$\frac{ax + b}{cx + d} = 2;$ $for$ $x$
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 $(a-2c)$
$\frac{x(a-2c)}{a-2c} = \frac{2d-b}{a-2c}$
$x = \frac{2d-b}{a-2c}$
