Solve:
#2/3x=3/8x+7/12#
Simplify #2/3x to (2x)/3#, and #3/8x to (3x)/8#.
#(2x)/3=(3x)/8+7/12#
Determine the least common denominator (LCD).
#3:##3,6,9,12,15,18,21,color(red)24,27...#
#8:##8,16,color(red)24...#
#12:##12,color(red)24...#
The LCD is #24#.
Multiply both sides by #24#.
#24xx(2x)/3=(24xx(3x)/8)+(24xx7/12)#
Simplify.
#color(red)cancel(color(black)(24^8))xx(2x)/color(red)cancel(color(black)(3^1))=(color(red)cancel(color(black)(24^3))xx(3x)/color(red)cancel(color(black)(8^1)))+(color(red)cancel(color(black)(24^2))xx7/color(red)cancel(color(black)(12^1)))#
#16x=9x+14#
Subtract #9x# from both sides.
#16x-9x=14#
Simplify.
#7x=14#
Divide both sides by #7#.
#x=14/7#
Simplify.
#x=2#
