How do you solve #\frac{x + 3}{2} + \frac{x + 5}{3} = \frac{2}{5}#?

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Answer 1 · 2016-09-24T20:04:44

#x = -83/25 = -3 8/25#

In an equation which has fractions, we can get rid of the denominators by multiplying through by the LCD.
The denominators will each cancel.

#\frac{x + 3}{2} + \frac{x + 5}{3} = \frac{2}{5}" "rarr LCD = color(red)(30)#

#(color(red)(60xx)(x + 3))/2 + (color(red)(60xx)(x+5))/3 = (color(red)(60xx)2)/5#

#(color(red)(cancel60^30xx)(x + 3))/cancel2 + (color(red)(cancel60^20xx)(x+5))/cancel3 = (color(red)(cancel60^12xx)2)/cancel5#

#30(x+3)+20(x+5) = 24" "larr# no fractions!

#30x+90 + 20x+100 = 24" "larr# remove brackets

#50x = 24-190" "larr# re-arrange the terms

#50x = -166#

#x = -166/50#

#x = -83/25#