How do you solve #7= - \frac { 6} { w - 6}#?

1 Answer
Jim G.
Apr 13, 2017

#w=36/7#

Explanation:

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

#"Note that for " -6/(w-6)# the negative sign is attached to the numerator #color(red)" or "# denominator but #color(red)" not both"#

#rArr7/1=(-6)/(w-6)larrcolor(red)" attach - to numerator"#

#color(blue)"cross-multiplying"# gives.

#7(w-6)=-6#

#rArr7w-42=-6larr" distributing the bracket"#

add 42 to both sides.

#7wcancel(-42)cancel(+42)=-6+42#

#rArr7w=36#

divide both sides by 7

#(cancel(7) w)/cancel(7)=36/7#

#rArrw=36/7#

#color(blue)"As a check"#

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

#(-6)/(36/7-42/7)=(-6)/(-6/7)=-6xx-7/6=7=" left side"#

#rArrw=36/7" is the solution"#

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