Solve 1/2x+y+z-21/2=0rightarrow

$$\frac { 1 } { 2 } x + y + z - \frac { 21 } { 2 } = 0 \rightarrow$$

Solve for x

$$x=21-2z-2y$$

Steps for Solving Linear Equation

Subtract y from both sides. Anything subtracted from zero gives its negation.

$$\frac{1}{2}x+z-\frac{21}{2}=-y$$

Subtract z from both sides.

$$\frac{1}{2}x-\frac{21}{2}=-y-z$$

Add \frac{21}{2} to both sides.

$$\frac{1}{2}x=-y-z+\frac{21}{2}$$

The equation is in standard form.

$$\frac{1}{2}x=\frac{21}{2}-z-y$$

Multiply both sides by 2.

$$\frac{\frac{1}{2}x}{\frac{1}{2}}=\frac{\frac{21}{2}-z-y}{\frac{1}{2}}$$

Dividing by \frac{1}{2} undoes the multiplication by \frac{1}{2}.

$$x=\frac{\frac{21}{2}-z-y}{\frac{1}{2}}$$

Divide -y-z+\frac{21}{2} by \frac{1}{2} by multiplying -y-z+\frac{21}{2} by the reciprocal of \frac{1}{2}.

$$x=21-2z-2y$$

Solve for y

$$y=-\frac{x}{2}-z+\frac{21}{2}$$

Solution Steps

Subtract \frac{1}{2}x from both sides. Anything subtracted from zero gives its negation.

$$y+z-\frac{21}{2}=-\frac{1}{2}x$$

Subtract z from both sides.

$$y-\frac{21}{2}=-\frac{1}{2}x-z$$

Add \frac{21}{2} to both sides.

$$y=-\frac{1}{2}x-z+\frac{21}{2}$$