Solve y-z/2-x-3/6=2x-1/3

$$\frac{ y-z }{ 2 } - \frac{ x-3 }{ 6 } = \frac{ 2x-1 }{ 3 }$$

Solve for x

$$x=\frac{3y}{5}-\frac{3z}{5}+1$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 6, the least common multiple of 2,6,3.

$$3\left(y-z\right)-\left(x-3\right)=2\left(2x-1\right)$$

Use the distributive property to multiply 3 by y-z.

$$3y-3z-\left(x-3\right)=2\left(2x-1\right)$$

To find the opposite of x-3, find the opposite of each term.

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

Use the distributive property to multiply 2 by 2x-1.

$$3y-3z-x+3=4x-2$$

Subtract 4x from both sides.

$$3y-3z-x+3-4x=-2$$

Combine -x and -4x to get -5x.

$$3y-3z-5x+3=-2$$

Subtract 3y from both sides.

$$-3z-5x+3=-2-3y$$

Add 3z to both sides.

$$-5x+3=-2-3y+3z$$

Subtract 3 from both sides.

$$-5x=-2-3y+3z-3$$

Subtract 3 from -2 to get -5.

$$-5x=-5-3y+3z$$

The equation is in standard form.

$$-5x=-3y+3z-5$$

Divide both sides by -5.

$$\frac{-5x}{-5}=\frac{-3y+3z-5}{-5}$$

Dividing by -5 undoes the multiplication by -5.

$$x=\frac{-3y+3z-5}{-5}$$

Divide -5-3y+3z by -5.

$$x=\frac{3y}{5}-\frac{3z}{5}+1$$

Solve for y

$$y=\frac{5x}{3}+z-\frac{5}{3}$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 6, the least common multiple of 2,6,3.

$$3\left(y-z\right)-\left(x-3\right)=2\left(2x-1\right)$$

Use the distributive property to multiply 3 by y-z.

$$3y-3z-\left(x-3\right)=2\left(2x-1\right)$$

To find the opposite of x-3, find the opposite of each term.

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

Use the distributive property to multiply 2 by 2x-1.

$$3y-3z-x+3=4x-2$$

Add 3z to both sides.

$$3y-x+3=4x-2+3z$$

Add x to both sides.

$$3y+3=4x-2+3z+x$$

Combine 4x and x to get 5x.

$$3y+3=5x-2+3z$$

Subtract 3 from both sides.

$$3y=5x-2+3z-3$$

Subtract 3 from -2 to get -5.

$$3y=5x-5+3z$$

The equation is in standard form.

$$3y=5x+3z-5$$

Divide both sides by 3.

$$\frac{3y}{3}=\frac{5x+3z-5}{3}$$

Dividing by 3 undoes the multiplication by 3.

$$y=\frac{5x+3z-5}{3}$$

Divide 5x-5+3z by 3.

$$y=\frac{5x}{3}+z-\frac{5}{3}$$