How do you solve #\frac{1}{2} x + \frac{1}{5} = - 5( \frac{4}{5} x + 2)#?

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Answer 1 · 2016-09-27T07:54:57

#x = -102/45#

#\frac{1}{2} x + \frac{1}{5} = color(blue)(- 5( \frac{4}{5} x + 2))" "larr# remove the bracket

#\frac{1}{2} x + \frac{1}{5} = color(blue)(- cancel5xx4/cancel5x -10)#

#\frac{1}{2} x + \frac{1}{5} = - 4x-10" "larr xx 10# to cancel denominators

#color(red)(cancel10^5)(1/cancel2x) + color(red)(cancel10^2)(1/cancel5) = - 4x xx color(red)(10)-10xxcolor(red)(10)#

#5x+2 = -40x-100" "larr# no fractions !!

#5x+40x=-100-2#

#45x = -102#

#x = -102/45#