How do you solve #-\frac { 6} { y - 2} = - 5#?

1 Answer
Jim G.
Feb 18, 2017

#y=16/5#

Explanation:

One method is to multiply both sides of the equation by the denominator of the single fraction. That is (y -2)

#cancel((y-2))^1xx-6/cancel((y-2))^1=-5(y-2)#

#rArr-6=-5(y-2)#

distribute the bracket.

#-6=-5y+10#

subtract 10 from both sides.

#-6-10=-5ycancel(+10)cancel(-10)#

#rArr-5y=-16#

To solve for y, divide both sides by - 5

#(cancel(-5) y)/cancel(-5)=(-16)/(-5)#

#rArry=16/5#

#color(blue)"As a check"#

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

#-6/(16/5-2)=-6/(16/5-10/5)#

#color(white)(xxxxxxx)=-6/(6/5)#

#color(white)(xxxxxxx)=-cancel(6)^1xx5/cancel(6)^1#

#color(white)(xxxxxxx)=-5#

#rArry=16/5" is the solution"#

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