Solve 2u+1/y-2=1/2

$$\frac { 2 u + 1 } { y - 2 } = \frac { 1 } { 2 }$$

Solve for u

$$u=\frac{y-4}{4}$$

$$y\neq 2$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 2\left(y-2\right), the least common multiple of y-2,2.

$$2\left(2u+1\right)=y-2$$

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

$$4u+2=y-2$$

Subtract 2 from both sides.

$$4u=y-2-2$$

Subtract 2 from -2 to get -4.

$$4u=y-4$$

Divide both sides by 4.

$$\frac{4u}{4}=\frac{y-4}{4}$$

Dividing by 4 undoes the multiplication by 4.

$$u=\frac{y-4}{4}$$

Divide y-4 by 4.

$$u=\frac{y}{4}-1$$

Solve for y

$$y=4\left(u+1\right)$$

$$u\neq -\frac{1}{2}$$

Solution Steps

Variable y cannot be equal to 2 since division by zero is not defined. Multiply both sides of the equation by 2\left(y-2\right), the least common multiple of y-2,2.

$$2\left(2u+1\right)=y-2$$

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

$$4u+2=y-2$$

Swap sides so that all variable terms are on the left hand side.

$$y-2=4u+2$$

Add 2 to both sides.

$$y=4u+2+2$$

Add 2 and 2 to get 4.

$$y=4u+4$$

Variable y cannot be equal to 2.

$$y=4u+4\text{, }y\neq 2$$