How do you solve #\frac{2}{3}(\frac{5}{6}x+10)=x-2#?

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Answer 1 · 2017-11-19T04:12:14

#x=39/2#

Use the distributive property (#a(b+c)=a*b+a*c#):

#2/3*5/6x+2/3*10=x-2#

#cancel(2)/3*5/(cancel(6)3)x+2/3*10=x-2#

#5/9x+20/3=x-2#

Make all the denominators the same. This makes it easier, we can scratch off the denominator after they're all equated.

#(5x+60)/9=(9x-18)/9#

#5x+60=9x-18# (multiplied both sides by #9#)

#9x-18-5x=60#

#4x-18=60#

#4x=60+18#

#4x=78#

#x=78/4=39/2#