Solve {l}{3+x/2x=1/2x+2/3}{y=x}{text{Solvefor}ztext{where}}{z=y}

$$\left. \begin{array} { l } { \frac{3 + x}{2 x} = \frac{1}{2 x} + \frac{2}{3} }\\ { y = x }\\ { \text{Solve for } z \text{ where} } \\ { z = y } \end{array} \right.$$

Solve for x, y, z

$$z=6$$

Solution Steps

Consider the first equation. Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 6x, the least common multiple of 2x,3.

$$3\left(3+x\right)=3+6x\times \frac{2}{3}$$

Use the distributive property to multiply 3 by 3+x.

$$9+3x=3+6x\times \frac{2}{3}$$

Multiply 6 and \frac{2}{3} to get 4.

$$9+3x=3+4x$$

Subtract 4x from both sides.

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

Combine 3x and -4x to get -x.

$$9-x=3$$

Subtract 9 from both sides.

$$-x=3-9$$

Subtract 9 from 3 to get -6.

$$-x=-6$$

Divide both sides by -1.

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

Fraction \frac{-6}{-1} can be simplified to 6 by removing the negative sign from both the numerator and the denominator.

$$x=6$$

Consider the second equation. Insert the known values of variables into the equation.

$$y=6$$

Consider the third equation. Insert the known values of variables into the equation.

$$z=6$$

The system is now solved.

$$x=6 y=6 z=6$$