Solve 2u+1/3-z-2/2=2

$$\frac { 2 u + 1 } { 3 } - \frac { z - 2 } { 2 } = 2$$

Solve for u

$$u=\frac{3z}{4}+1$$

Steps for Solving Linear Equation

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

$$2\left(2u+1\right)-3\left(z-2\right)=12$$

Use the distributive property to multiply 2 by 2u+1.

$$4u+2-3\left(z-2\right)=12$$

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

$$4u+2-3z+6=12$$

Add 2 and 6 to get 8.

$$4u+8-3z=12$$

Subtract 8 from both sides.

$$4u-3z=12-8$$

Subtract 8 from 12 to get 4.

$$4u-3z=4$$

Add 3z to both sides.

$$4u=4+3z$$

The equation is in standard form.

$$4u=3z+4$$

Divide both sides by 4.

$$\frac{4u}{4}=\frac{3z+4}{4}$$

Dividing by 4 undoes the multiplication by 4.

$$u=\frac{3z+4}{4}$$

Divide 4+3z by 4.

$$u=\frac{3z}{4}+1$$

Solve for z

$$z=\frac{4\left(u-1\right)}{3}$$

Steps for Solving Linear Equation

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

$$2\left(2u+1\right)-3\left(z-2\right)=12$$

Use the distributive property to multiply 2 by 2u+1.

$$4u+2-3\left(z-2\right)=12$$

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

$$4u+2-3z+6=12$$

Add 2 and 6 to get 8.

$$4u+8-3z=12$$

Subtract 4u from both sides.

$$8-3z=12-4u$$

Subtract 8 from both sides.

$$-3z=12-4u-8$$

Subtract 8 from 12 to get 4.

$$-3z=4-4u$$

Divide both sides by -3.

$$\frac{-3z}{-3}=\frac{4-4u}{-3}$$

Dividing by -3 undoes the multiplication by -3.

$$z=\frac{4-4u}{-3}$$

Divide 4-4u by -3.

$$z=\frac{4u-4}{3}$$