How do you solve #\frac { 2} { 5} k + 1= \frac { 57} { 65}#?

1 Answer
smendyka
Dec 26, 2016

#k = -4/13#

Explanation:

First, multiple each side of the equation by #color(red)(65)# to eliminate the fractions and keep the equation balanced:

#color(red)(65)(2/5k + 1) = color(red)(65) xx 57/65#

#((color(red)(65) xx 2))/5k + (color(red)(65) xx 1) = color(red)(65) xx 57/65#

#((cancel(color(red)(65)) 13 xx 2))/color(red)(cancel(color(black)(5)))k + color(red)(65) = cancel(color(red)(65)) xx 57/color(red)(cancel(color(black)(65)))#

#26k + 65 = 57#

We can now subtract #color(blue)(65)# from each side of the equation to isolate the #k# term and keep the equation balanced:

#26k + 65 - color(blue)(65) = 57 - color(blue)(65)#

#26k + 0 = -8#

#26k = -8#

Now we can divide each side of the equation by #color(green)(26)# to solve for #k# while keeping the equation balanced:

#(26k)/color(green)(26) = -8/color(green)(26)#

#(color(green)(cancel(color(black)(26)))k)/cancel(color(green)(26)) = -(4 xx 2)/(13 xx 2)#

#k = -(4 xx color(red)(cancel(color(black)(2))))/(13 xx color(red)(cancel(color(black)(2))))#

#k = -4/13#

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