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


Answered 4 months ago
Answered 4 months ago
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Work as shown below, follow the steps:

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

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

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

ax2cx=2db\Rightarrow ax-2cx=2d-b\qquad\qquad\qquad\qquad\qquad\quad $\color{#c34632} \text{[factor out xx] }$

x(a2c)=2db\Rightarrow x(a-2c)=2d-b\qquad\qquad\qquad\qquad $\color{#c34632}\text{[divide both sides by a2ca-2c]}$

x=2dba2c\Rightarrow \color{#4257b2} \text{$x=\dfrac{2d-b}{a-2c}$}

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