What is the solution to the equation 1/2x+3=2/3x+1?

Question

kevin · Answer

step 1: remove denominator by multiply both side with denominator least common multiple
step 2 : move number contains x to left and the other to right
step 3 : simplify the equation

done

cmdrwinters · Answer

To solve this, we must first isolate the variable on one side of the equation.

$$\frac{ 1 }{ 2 }x + 3 = \frac{ 2 }{ 3 }x + 1$$

First step in this process would be to combine the like terms on their own side of the equation. 


$$\frac{ 1 }{ 2 }x + 3 - 3= \frac{ 2 }{ 3 }x + 1-3 $$


$$\frac{ 1 }{ 2 }x = \frac{ 2 }{ 3 }x -2 $$


$$\frac{ 1 }{ 2 }x -\frac{ 2 }{ 3 }x= \frac{ 2 }{ 3 }x - \frac{ 2 }{ 3 }x -2 $$

At this point we can find a common denominator to make simplifying the fractions much easier. The lowest common denominator for these fractions would be 6, so we can make it


$$\frac{ 3 }{ 6 }x -\frac{ 4 }{ 6 }x= \frac{ 4 }{ 6 }x - \frac{ 4 }{ 6 }x -2 $$


$$ -\frac{ 1 }{ 6 }x=  -2 $$

Now, we just divide both sides by the fraction to find the variable.

$$ -\frac{ 1 }{ 6 }x / -\frac{ 1 }{ 6 } =  -2/-\frac{ 1 }{ 6 } $$

$$ x =12$$

Which is our answer.
Hope that helped! :)

jhonyy9 · Answer

please use parentheses bc. not is clearly what mean denominator 2x or 2x +3 and on the other side 3x or 3x +1 ?