Calculate: (x+3)/(2)=(2x+1)/(3)

Expression: $\frac{ x+3 }{ 2 }=\frac{ 2x+1 }{ 3 }$

Move the expression to the left-hand side and change its sign

$\frac{ x+3 }{ 2 }-\frac{ 2x+1 }{ 3 }=0$

Multiply both sides of the equation by $6$

$3\left( x+3 \right)-2\left( 2x+1 \right)=0$

Distribute $3$ through the parentheses

$3x+9-2\left( 2x+1 \right)=0$

Distribute $-2$ through the parentheses

$3x+9-4x-2=0$

Collect like terms

$-x+9-2=0$

Subtract the numbers

$-x+7=0$

Change the signs on both sides of the equation

$x-7=0$