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Solve for X.

a/b(2x - 12) = c/d

Guest Aug 20, 2017
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#1
+178
+2

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 :)

Jeffes02  Aug 20, 2017
#2
+6897
+2

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!

!

asinus  Aug 20, 2017
#3
+178
+2

Good work of yours! It is really easily for people to confuse others with inappropiate use of brackets.

Jeffes02  Aug 20, 2017
#4
+6897
+1

If I mean $$\frac{a}{b}(2x-12)=\frac{c}{d}$$, I should write (a/b)*(2x - 12) = c/d.

If I mean $$\frac{a}{b(2x-12)}=\frac{c}{d}$$, I should write a/(b(2x - 12)) = c/d.
This is not unreasonable.

a/b(2x - 12) = c/d  can mean both.

asinus  Aug 20, 2017

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