How do you solve #\frac { 2} { 3} = \frac { z - 3} { 2}#?

1 Answer
smendyka
Feb 2, 2017

See the entire solution process below:

Explanation:

First, multiply each side of the equation by #color(red)(6)# to eliminate the fractions and keep the equation balanced. #color(red)(6)# is the lowest common denominator of the two fractions and eliminating the fractions will make the problem easier to work.

#color(red)(6) xx 2/3 = color(red)(6) xx (z - 3)/2#

#12/3 = cancel(color(red)(6))3 xx (z - 3)/color(red)(cancel(color(black)(2)))#

#4 = 3z - 9#

Next, add #color(red)(9)# to each side of the equation to isolate the #z# term while keeping the equation balanced:

#4 + color(red)(9) = 3z - 9 + color(red)(9)#

#13 = 3z - 0#

#13 = 3z#

Now, divide each side of the equation by #color(red)(3)# to solve for #z# while keeping the equation balanced:

#13/color(red)(3) = (3z)/color(red)(3)#

#13/3 = (color(red)(cancel(color(black)(3)))z)/cancel(color(red)(3))#

#13/3 = z#

#z = 13/3#

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