Question 219124
Is the equation {{{2x+1/3=2x-1/2}}} ???


{{{2x+1/3=2x-1/2}}} Start with the given equation.



{{{6(2x+1/cross(3))=6(2x-1/cross(2))}}} Multiply both sides by the LCD {{{6}}} to clear any fractions.



{{{12x+2=12x-3}}} Distribute and multiply.



{{{12x=12x-3-2}}} Subtract {{{2}}} from both sides.



{{{12x-12x=-3-2}}} Subtract {{{12x}}} from both sides.



{{{0x=-3-2}}} Combine like terms on the left side.



{{{0x=-5}}} Combine like terms on the right side.



{{{0=-5}}} Simplify.



Since this equation is <font size=4><b>never</b></font> true for any x value, this means that there are no solutions.


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OR...



Is the equation {{{(2x+1)/3=(2x-1)/2}}} ???



{{{(2x+1)/3=(2x-1)/2}}} Start with the given equation.



{{{2(2x+1)=3(2x-1)}}} Cross multiply.



{{{4x+2=6x-3}}} Distribute.



{{{4x=6x-3-2}}} Subtract {{{2}}} from both sides.



{{{4x-6x=-3-2}}} Subtract {{{6x}}} from both sides.



{{{-2x=-3-2}}} Combine like terms on the left side.



{{{-2x=-5}}} Combine like terms on the right side.



{{{x=(-5)/(-2)}}} Divide both sides by {{{-2}}} to isolate {{{x}}}.



{{{x=5/2}}} Reduce.



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Answer:


So the solution is {{{x=5/2}}} which in decimal form is {{{x=2.5}}}.