Solve:
#9/16x-5/3<5/6x+8/3#
Simplify #9/16x# to #(9x)/16#.
#(9x)/16-5/3<5/6x+8/3#
Simplify #5/6x# to #(5x)/6#.
#(9x)/16-5/3<(5x)/6+8/3#
In order to add or subtract fractions, the denominators must be the same. We can use prime factorization to determine the LCD.
#3=3^1#
#6=2xx3#
#16=2^4#
Multiply the prime factors with the largest exponents.
LCD: #3^1xx2^4=48#
Multiply both sides of the inequality by #48#. This will make all denominators #1#.
#(color(red)cancel(color(black)(48))^3xx(9x)/color(red)cancel(color(black)(16))^1)-(color(red)cancel(color(black)(48))^16xx5/color(red)cancel(color(black)(3))^1)<(color(red)cancel(color(black)(48))^8xx(5x)/color(red)cancel(color(black)(6))^1)+(color(red)cancel(color(black)(48))^16xx8/color(red)cancel(color(black)(3))^1)#
Simplify.
#27x-80<40x+128#
Subtract #27x# from both sides.
#-80<40x+128-27x#
Simplify.
#-80<13x+128#
Subtract #128# from both sides.
#-80-128<13x#
Simplify.
#-208<13x#
Divide both sides by #13#.
#-208/13##<##x#
Simplify.
#-16##<##x#
Switch sides.
#x<-16#
