Solve for b a=1/2(a+b)

$a = \frac{1}{2} (a + b)$

Rewrite the equation as $\frac{1}{2} \cdot (a + b) = a$ .

$\frac{1}{2} \cdot (a + b) = a$

Multiply both sides of the equation by $2$ .

$2 (\frac{1}{2} \cdot (a + b)) = 2 a$

Simplify the left side.

Simplify $2 (\frac{1}{2} \cdot (a + b))$ .

Apply the distributive property.

$2 (\frac{1}{2} a + \frac{1}{2} b) = 2 a$

Combine $\frac{1}{2}$ and $a$ .

$2 (\frac{a}{2} + \frac{1}{2} b) = 2 a$

Combine $\frac{1}{2}$ and $b$ .

$2 (\frac{a}{2} + \frac{b}{2}) = 2 a$

Apply the distributive property.

$2 \frac{a}{2} + 2 \frac{b}{2} = 2 a$

Cancel the common factor of $2$ .

Cancel the common factor.

$2 \frac{a}{2} + 2 \frac{b}{2} = 2 a$

Rewrite the expression.

$a + 2 \frac{b}{2} = 2 a$

Cancel the common factor of $2$ .

Cancel the common factor.

$a + 2 \frac{b}{2} = 2 a$

Rewrite the expression.

$a + b = 2 a$

Move all terms not containing $b$ to the right side of the equation.

Subtract $a$ from both sides of the equation.

$b = 2 a - a$

Subtract $a$ from $2 a$ .

$b = a$