Calculate: (2x+7)/(3)-(x-3)/(2)=4x

Expression: $\frac{ 2x+7 }{ 3 }-\frac{ x-3 }{ 2 }=4x$

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

$\frac{ 2x+7 }{ 3 }-\frac{ x-3 }{ 2 }-4x=0$

Multiply both sides of the equation by $6$

$2\left( 2x+7 \right)-3\left( x-3 \right)-24x=0$

Distribute $2$ through the parentheses

$4x+14-3\left( x-3 \right)-24x=0$

Distribute $-3$ through the parentheses

$4x+14-3x+9-24x=0$

Collect like terms

$-23x+14+9=0$

Add the numbers

$-23x+23=0$

Move the constant to the right-hand side and change its sign

$-23x=-23$

Divide both sides of the equation by $-23$

$x=1$