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

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

Solve for u

$$u=-\frac{2}{3}\approx -0.666666667$$

Steps for Solving Linear Equation

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

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

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

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

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

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

Subtract 2u from both sides.

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

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

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

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

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

Since -\frac{1}{2} and \frac{3}{2} have the same denominator, add them by adding their numerators.

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

Add -1 and 3 to get 2.

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

Divide 2 by 2 to get 1.

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

Multiply both sides by -\frac{2}{3}, the reciprocal of -\frac{3}{2}.

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

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

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