## Related questions with answers

Question

Solve the equation for the indicated variable. $\frac{a x+b}{c x+d}=2;$ for x

Solution

VerifiedAnswered 4 months ago

Answered 4 months ago

Step 1

1 of 2Work as shown below, follow the steps:

$\dfrac{ax+b}{cx+d}=2\qquad\qquad\qquad\qquad\qquad\qquad\qquad$ $\color{#c34632} \text{[cross multiplication]}$

$\Rightarrow ax+b=2(cx+d)$

$\Rightarrow ax+b=2cx+2d\qquad\qquad\qquad\qquad\qquad$ $\color{#c34632} \text{[match like terms]}$

$\Rightarrow ax-2cx=2d-b\qquad\qquad\qquad\qquad\qquad\quad$ $\color{#c34632} \text{[factor out $x$] }$

$\Rightarrow x(a-2c)=2d-b\qquad\qquad\qquad\qquad$ $\color{#c34632}\text{[divide both sides by $a-2c$]}$

$\Rightarrow \color{#4257b2} \text{$x=\dfrac{2d-b}{a-2c}$}$

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