Advanced Algebra

Input: Solve for X. a/b(2x - 12) = c/d

Intepretation: Solve for $x$ in $\frac{a}{b}(2x-12)=\frac{c}{d}$

Solution:

Multiple both sides by $bd$:

$ad(2x-12)=bc$

Expand:

$2adx-12ad=bc$

Move the numerical term to the right:

$2adx=12ad+bc$

Divide both sides by $2$
$adx=6ad+\frac{bc}{2}$

Finally, divide both sides by a factor of $ad$:

$x=6+\frac{bc}{2ad}$

Done :)

Solve for X.
a/b(2x - 12) = c/d

1.                                            on both sides

$\frac{a}{b}(2x - 12) = \frac{c}{d}$                 [$\times\frac{b}{a}$

$2x-12=\frac{bc}{ad}$                      [+12       

$2x=\frac{bc}{ad}+12$                      [ / 2

$x=\frac{bc}{2ad}+6$ 

2.

$\frac{a}{b(2x-12)}=\frac{c}{d}$                        [$\times (2x-12)$ 

$\frac{a}{b}=\frac{c}{d}(2x-12)$                 [$\times\frac{d}{c}$

$\frac{ad}{bc}=2x-12$                      [+12

$\frac{ad}{bc}+12=2x$                      [ / 2

$\frac{ad}{2bc}+6=x$

$x=\frac{ad}{2bx}+6$

Both can be meant. Use brackets!

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