Question

How do I solve this1/2x + 3 = 2/3x + 1

Answer 1

Step-by-step explanation:

Given the expression:

`(1)/(2x)+3=(2)/(3x)+1`

To solve this, first collect the like terms as:

`\begin{gathered} (1)/(2x)-(2)/(3x)=1-3 \\ \\ (1)/(2x)-(1)/(3x)=-2 \end{gathered}`

Next, we can multiply both sides of the equation by 6x to nullify the fractions on the left-hand side

`\begin{gathered} (6x)/(2x)-(6x)/(3x)=-2*12x \\ \\ 3-2=-24x \\ \\ 1=-24x \end{gathered}`

Finally, divide both sides by the coefficient of x, which is -24

`\begin{gathered} x=(1)/(-24) \\ \\ x=-(1)/(24) \end{gathered}`