Solve:
#(x-3)/3+(x+2)/2=34#
Multiply both sides by the GCF #6#.
#(color(red)cancel(color(black)(6^2))(x-3))/3+(color(red)cancel(color(black)(6^3))(x+2))/2=34xx6#
Simplify.
#2(x-3)+3(x+2)=204#
Expand using the distributive property: #a(b+c)=ab+ac#
#2x-6+3x+6=204#
Simplify.
#2x-color(red)cancel(color(black)(6))+3x+color(red)cancel(color(black)(6))=204#
Simplify.
#2x+3x=204#
#5x=204#
Divide both sides by #5#.
#(5x)/5=204/5#
Simplify.
#(color(red)cancel(color(black)(5^1))x)/color(red)cancel(color(black)(5^1))=204/5#
#x=204/5#
You can convert #204/5# to a mixed fraction by dividing #204# by #5#. The whole number is the quotient and the remainder is the numerator over the denominator of #5#.
#204-:5=40# with a remainder of #4#
As a mixed fraction, #x=40 4/5#.
