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

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

Step 1

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

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

Step 2

Multiply both sides of the equation by $2$ .

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

Step 3

Simplify the left side.

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

$h (a + b) = 2 a$

Apply the distributive property.

$h a + h b = 2 a$

Step 4

Subtract $h a$ from both sides of the equation.

$h b = 2 a - h a$

Step 5

Divide each term in $h b = 2 a - h a$ by $h$ and simplify.

Divide each term in $h b = 2 a - h a$ by $h$ .

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

Simplify the left side.

Cancel the common factor of $h$ .

Cancel the common factor.

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

Divide $b$ by $1$ .

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

Simplify the right side.

Simplify each term.

Cancel the common factor of $h$ .

Cancel the common factor.

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

Divide $- 1 a$ by $1$ .

$b = \frac{2 a}{h} - 1 a$

Rewrite $- 1 a$ as $- a$ .

$b = \frac{2 a}{h} - a$