How do you solve #\frac { 6( 7- z ) } { 5} = - z#?

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Answer 1 · 2017-02-04T23:12:50

See the entire solution process below:

First, multiply each side of the equation by #color(red)(5)# to eliminate the fraction while keeping the equation balanced:

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

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

#6(7 - z) = -5z#

Next, expand the terms in parenthesis on the left side of the equation.

#(6 xx 7) - (6 xx z) = -5z#

#42 - 6z = -5z#

Now, add #color(red)(6z)# to each side of the equation to solve for #z# while keeping the equation balanced:

#42 - 6z + color(red)(6z) = -5z + color(red)(6z)#

#42 - 0 = (-5 + 6)z#

#42 = 1z#

#z = 42#