How do you solve \frac{x + 3}{2} + \frac{x + 5}{3} = \frac{2}{5}x+32+x+53=25?

1 Answer
Sep 24, 2016

x = -83/25 = -3 8/25x=8325=3825

Explanation:

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)x+32+x+53=25 LCD=30

(color(red)(60xx)(x + 3))/2 + (color(red)(60xx)(x+5))/3 = (color(red)(60xx)2)/560×(x+3)2+60×(x+5)3=60×25

(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