How do you solve #-\frac { 4} { 3} - \frac { 6} { 7} x = - \frac { 1} { 2}#?

1 Answer
smendyka
Sep 8, 2017

See a solution process below:

Explanation:

First, add #color(red)(4/3)# to each side of the equation to isolate the #x# term while keeping the equation balanced:

#color(red)(4/3) - 4/3 - 6/7x = color(red)(4/3) - 1/2#

#0 - 6/7x = (2/2 xx color(red)(4/3)) - (3/3 xx 1/2)#

#-6/7x = color(red)(8/6) - 3/6#

#-6/7x = (color(red)(8) - 3)/6#

#-6/7x = 5/6#

Next, multiply each side of the equation by #color(red)(7)/color(blue)(-6)# to solve for #x# while keeping the equation balanced:

#color(red)(7)/color(blue)(-6) xx (-6)/7x = color(red)(7)/color(blue)(-6) xx 5/6#

#cancel(color(red)(7))/cancel(color(blue)(-6)) xx color(blue)(cancel(color(black)(-6)))/color(red)(cancel(color(black)(7)))x = (color(red)(7) xx 5)/(color(blue)(-6) xx 6)#

#x = 35/-36#

#x = -35/36#

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