How do you solve #\frac { 2x + 12} { 3x - 6} = \frac { 10} { 11}#?

1 Answer
smendyka
Jul 27, 2017

See a solution process below:

Explanation:

First do a cross product or cross multiply the equation:

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#11(2x + 12) = 10(3x - 6)#

Next, expand the terms in parenthesis on each side of the equation by multiplying each of the terms within the parenthesis by the term outside the parenthesis:

#color(red)(11)(2x + 12) = color(blue)(10)(3x - 6)#

#(color(red)(11) xx 2x) + (color(red)(11) xx 12) = (color(blue)(10) xx 3x) - (color(blue)(10) xx 6)#

#22x + 132 = 30x - 60#

Then, subtract #color(red)(22x)# and add #color(blue)(60)# to each side of the equation to isolate the #x# term while keeping the equation balanced:

#-color(red)(22x) + 22x + 132 + color(blue)(60) = -color(red)(22x) + 30x - 60 + color(blue)(60)#

#0 + 192 = (-color(red)(22) + 30)x - 0#

#192 = 8x#

Now, divide each side of the equation by #color(red)(8)# to solve for #x# while keeping the equation balanced:

#192/color(red)(8) = (8x)/color(red)(8)#

#24 = x#

#x = 24#

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