Solve 4-z/2-x-3/6=2x-3/3

$$\frac { 4 - z } { 2 } - \frac { x - 3 } { 6 } = \frac { 2 x - 3 } { 3 }$$

Solve for x

$$x=\frac{21-3z}{5}$$

Steps for Solving Linear Equation

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

$$3\left(4-z\right)-\left(x-3\right)=2\left(2x-3\right)$$

Use the distributive property to multiply 3 by 4-z.

$$12-3z-\left(x-3\right)=2\left(2x-3\right)$$

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

$$12-3z-x+3=2\left(2x-3\right)$$

Add 12 and 3 to get 15.

$$15-3z-x=2\left(2x-3\right)$$

Use the distributive property to multiply 2 by 2x-3.

$$15-3z-x=4x-6$$

Subtract 4x from both sides.

$$15-3z-x-4x=-6$$

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

$$15-3z-5x=-6$$

Subtract 15 from both sides.

$$-3z-5x=-6-15$$

Subtract 15 from -6 to get -21.

$$-3z-5x=-21$$

Add 3z to both sides.

$$-5x=-21+3z$$

The equation is in standard form.

$$-5x=3z-21$$

Divide both sides by -5.

$$\frac{-5x}{-5}=\frac{3z-21}{-5}$$

Dividing by -5 undoes the multiplication by -5.

$$x=\frac{3z-21}{-5}$$

Divide -21+3z by -5.

$$x=\frac{21-3z}{5}$$

Solve for z

$$z=-\frac{5x}{3}+7$$

Steps for Solving Linear Equation

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

$$3\left(4-z\right)-\left(x-3\right)=2\left(2x-3\right)$$

Use the distributive property to multiply 3 by 4-z.

$$12-3z-\left(x-3\right)=2\left(2x-3\right)$$

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

$$12-3z-x+3=2\left(2x-3\right)$$

Add 12 and 3 to get 15.

$$15-3z-x=2\left(2x-3\right)$$

Use the distributive property to multiply 2 by 2x-3.

$$15-3z-x=4x-6$$

Subtract 15 from both sides.

$$-3z-x=4x-6-15$$

Subtract 15 from -6 to get -21.

$$-3z-x=4x-21$$

Add x to both sides.

$$-3z=4x-21+x$$

Combine 4x and x to get 5x.

$$-3z=5x-21$$

Divide both sides by -3.

$$\frac{-3z}{-3}=\frac{5x-21}{-3}$$

Dividing by -3 undoes the multiplication by -3.

$$z=\frac{5x-21}{-3}$$

Divide 5x-21 by -3.

$$z=-\frac{5x}{3}+7$$