Question 196882
{{{(3x+2)/4=9/4-(3-2x)/6}}} Start with the given equation.



{{{cross(12)^3((3x+2)/cross(4))=cross(12)^3(9/cross(4))-cross(12)^2((3-2x)/cross(6))}}} Multiply EVERY term by the LCD 12 to clear out the fractions.



{{{3(3x+2)=3(9)-2(3-2x)}}} Simplify



{{{3(3x+2)=27-2(3-2x)}}} Multiply



{{{9x+6=27-6+4x}}} Distribute.



{{{9x+6=4x+21}}} Combine like terms on the right side.



{{{9x=4x+21-6}}} Subtract {{{6}}} from both sides.



{{{9x-4x=21-6}}} Subtract {{{4x}}} from both sides.



{{{5x=21-6}}} Combine like terms on the left side.



{{{5x=15}}} Combine like terms on the right side.



{{{x=(15)/(5)}}} Divide both sides by {{{5}}} to isolate {{{x}}}.



{{{x=3}}} Reduce.



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Answer:


So the solution is {{{x=3}}}