How do you solve #-2\frac { 1} { 6} x + \frac { 3} { 5} x = - \frac { 47} { 105}#?

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Answer 1 · 2017-08-29T14:29:08

#x = 2/7#

#-2 1/6x +3/5x = -47/105#

Write the mixed number as an improper fraction first.

#(-13x)/6+ (3x)/5 = -47/105#

To get rid of all the denominators in the equation, multiply each term by the LCM of the denominators.

This is #210#, made up of the prime factors of #" "2xx3xx5xx7#

#(-13x color(blue)(xxcancel210^35))/cancel6+ (3x color(blue)(xxcancel210^42))/cancel5 = (-47color(blue)(xxcancel210^2))/cancel105" "larr# cancel

#-455x +126x = -94#

#-329x = -94" "larr div -329#

#(-329x)/(-329) = (-94)/(-329)#

#x = 2/7#