Answer:
Explanation:
Given the expression:
[tex]\frac{1}{2x}+3=\frac{2}{3x}+1[/tex]To solve this, first collect the like terms as:
[tex]\begin{gathered} \frac{1}{2x}-\frac{2}{3x}=1-3 \\ \\ \frac{1}{2x}-\frac{1}{3x}=-2 \end{gathered}[/tex]Next, we can multiply both sides of the equation by 6x to nullify the fractions on the left-hand side
[tex]\begin{gathered} \frac{6x}{2x}-\frac{6x}{3x}=-2\times12x \\ \\ 3-2=-24x \\ \\ 1=-24x \end{gathered}[/tex]Finally, divide both sides by the coefficient of x, which is -24
[tex]\begin{gathered} x=\frac{1}{-24} \\ \\ x=-\frac{1}{24} \end{gathered}[/tex]
