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

2 Answers
Sonnhard
Jun 1, 2018

#z=77#

Explanation:

By cross multiplication we get
#6(z-7)=5(z+7)#
expanding
#6z-42=5z+35#
so
#z=77#

Jim G.
Jun 1, 2018

#z=77#

Explanation:

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

#•color(white)(x)a/b=c/drArrad=bc#

#6(z-7)=5(z+7)larrcolor(blue)"distribute"#

#6z-42=5z+35#

#"subtract "5z" from both sides"#

#6z-5z-42=cancel(5z)cancel(-5z)+35#

#z=42=35#

#"add 42 to both sides"#

#z=35+42=77#

#color(blue)"As a check"#

Substitute this value into the equation and if both sides are equal then it is the solution.

#"left "=6/(77+7)=6/84=1/14#

#"right "=5/(77-7)=5/70=1/14#

#"thus "x=77" is the solution"#

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