Try Magic Notes and save time.Try it free
Try Magic Notes and save timeCrush your year with the magic of personalized studying.Try it free
Question

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

Solution

Verified
Step 1
1 of 2

Work 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 $a-2c$]}$

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

## Recommended textbook solutions

#### Precalculus

2nd EditionISBN: 9780076602186Carter, Cuevas, Day, Malloy
8,886 solutions

#### Nelson Functions 11

1st EditionISBN: 9780176332037Chris Kirkpatrick, Marian Small
1,275 solutions

#### Precalculus with Limits

3rd EditionISBN: 9781133962885 (3 more)Larson
11,142 solutions

#### Precalculus: Mathematics for Calculus

7th EditionISBN: 9781305071759 (5 more)Lothar Redlin, Stewart, Watson
9,606 solutions