Solve x=x/2+2/3*x/2+500

$$x = \frac { x } { 2 } + \frac { 2 } { 3 } \cdot \frac { x } { 2 } + 500$$

Solve for x

$$x=3000$$

Steps for Solving Linear Equation

Multiply \frac{2}{3} times \frac{x}{2} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{x}{2}+\frac{2x}{3\times 2}+500$$

Cancel out 2 in both numerator and denominator.

$$x=\frac{x}{2}+\frac{x}{3}+500$$

Combine \frac{x}{2} and \frac{x}{3} to get \frac{5}{6}x.

$$x=\frac{5}{6}x+500$$

Subtract \frac{5}{6}x from both sides.

$$x-\frac{5}{6}x=500$$

Combine x and -\frac{5}{6}x to get \frac{1}{6}x.

$$\frac{1}{6}x=500$$

Multiply both sides by 6, the reciprocal of \frac{1}{6}.

$$x=500\times 6$$

Multiply 500 and 6 to get 3000.

$$x=3000$$