SOLUTION: Solve for x a/b(2x-12)=c/d

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Question 150860This question is from textbook Prentice Hall Algebra II
: Solve for x
a/b(2x-12)=c/d This question is from textbook Prentice Hall Algebra II

Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!

Which do you mean?

This:

%28a%2Fb%29%282x-12%29=c%2Fd

or this:

a%2Fb%282x-12%29=c%2Fd

????

If you meant this:

%28a%2Fb%29%282x-12%29=c%2Fd

Clear of fractions by multiplying both sides by bd

%28bd%29%2A%28a%2Fb%29%282x-12%29=%28bd%29%2A%28c%2Fd%29



ad%282x-12%29=bc

ad%2A2x-ad%2A12=bc

2adx-12ad=bc

Get the term in x on one side by itself, or
as they sometimes say, isolate the term with x.
I'll isolate it on the left:

2adx=bc%2B12ad

Solve for x by dividing both sides of the equation by
what is multiplied by x, namely 2ad

%282adx%29%2F%282ad%29=%28bc%2B12ad%29%2F%282ad%29

%28cross%282ad%29x%29%2F%28cross%282ad%29%29=%28bc%2B12ad%29%2F%282ad%29

x=%28bc%2B12ad%29%2F%282ad%29

Warning! Leave the answer like that!  Don't think you can
do any canceling on the right for you cannot! The 12ad
is ADDED not MULTIPLIED.

---------------------------------------------------

If you meant this:

a%2Fb%282x-12%29=c%2Fd

Clear of fractions by multiplying both sides by b%282x-12%29
a shortcut for which is known as cross-multiplying:

ad=bc%282x-12%29

ad=2bcx-12bc

Get the term in x on one side by itself, or
as they sometimes say, isolate the term with x.
I'll isolate it on the right this time:

ad%2B12bc=2bcx

Solve for x by dividing both sides of the equation by
what is multiplied by x, namely 2bc

%28ad%2B12bc%29%2F%282bc%29=%282bcx%29%2F%282bc%29

%28ad%2B12bc%29%2F%282bc%29=%28cross%282bc%29x%29%2Fcross%282bc%29

%28ad%2B12bc%29%2F%282bc%29=x

or if you don't like x on the right, then write it
on the left :-)

x=%28ad%2B12bc%29%2F%282bc%29

Warning! As before, leave the answer like that!  Don't think 
you can do any canceling for you cannot! The 12bc
in the numerator is ADDED, not MULTIPLIED.

Edwin