Solve 1/2(u-3)=2u-3/2

$$\frac { 1 } { 2 } ( u - 3 ) = 2 u - \frac { 3 } { 2 }$$

Solve for u

$$u=0$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{1}{2} by u-3.

$$\frac{1}{2}u+\frac{1}{2}\left(-3\right)=2u-\frac{3}{2}$$

Multiply \frac{1}{2} and -3 to get \frac{-3}{2}.

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

Fraction \frac{-3}{2} can be rewritten as -\frac{3}{2} by extracting the negative sign.

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

Subtract 2u from both sides.

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

Combine \frac{1}{2}u and -2u to get -\frac{3}{2}u.

$$-\frac{3}{2}u-\frac{3}{2}=-\frac{3}{2}$$

Add \frac{3}{2} to both sides.

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

Add -\frac{3}{2} and \frac{3}{2} to get 0.

$$-\frac{3}{2}u=0$$

Product of two numbers is equal to 0 if at least one of them is 0. Since -\frac{3}{2} is not equal to 0, u must be equal to 0.

$$u=0$$