How do you solve #\frac { z + 6} { z - 7} = \frac { 8} { - 7}#?

1 Answer
Jim G.
May 13, 2018

#z=14/15#

Explanation:

#"one way is to use "color(blue)"cross-multiplication"#

#•color(white)(x)a/b=c/drArrad=bc#

#rArr8(z-7)=-7(z+6)#

#"distribute brackets on both sides"#

#8z-56=-7z-42#

#"add "7z" to both sides"#

#8z+7z-56=cancel(-7z)cancel(+7z)-42#

#rArr15z-56=-42#

#"add 56 to both sides"#

#15zcancel(-56)cancel(+56)=-42+56#

#rArr15z=14#

#"divide both sides by 15"#

#(cancel(15) z)/cancel(15)=14/15#

#rArrz=14/15#

#color(blue)"As a check"#

Substitute this value into the left side of the equation and if equal to the right side then it is the solution.

#(14/15+90/15)/(14/15-105/15)#

#=(104/15)/(-91/15)=104/cancel(15)xx-cancel(15)/91=-104/91=-8/7#

#rArrz=14/15" is the solution"#

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