Solve for x A=1/2h(x+y)

$A = \frac{1}{2} h (x + y)$

Step 1

Rewrite the equation as $\frac{1}{2} \cdot (h (x + y)) = A$ .

$\frac{1}{2} \cdot (h (x + y)) = A$

Step 2

Multiply both sides of the equation by $2$ .

$2 (\frac{1}{2} \cdot (h (x + y))) = 2 A$

Step 3

Simplify the left side.

Simplify $2 (\frac{1}{2} \cdot (h (x + y)))$ .

Apply the distributive property.

$2 (\frac{1}{2} \cdot (h x + h y)) = 2 A$

Apply the distributive property.

$2 (\frac{1}{2} (h x) + \frac{1}{2} (h y)) = 2 A$

Multiply $\frac{1}{2} (h x)$ .

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

$2 (\frac{h}{2} x + \frac{1}{2} (h y)) = 2 A$

Combine $\frac{h}{2}$ and $x$ .

$2 (\frac{h x}{2} + \frac{1}{2} (h y)) = 2 A$

$2 (\frac{h x}{2} + \frac{1}{2} (h y)) = 2 A$

Multiply $\frac{1}{2} (h y)$ .

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

$2 (\frac{h x}{2} + \frac{h}{2} y) = 2 A$

Combine $\frac{h}{2}$ and $y$ .

$2 (\frac{h x}{2} + \frac{h y}{2}) = 2 A$

$2 (\frac{h x}{2} + \frac{h y}{2}) = 2 A$

Apply the distributive property.

$2 \frac{h x}{2} + 2 \frac{h y}{2} = 2 A$

Cancel the common factor of $2$ .

Cancel the common factor.

$2 \frac{h x}{2} + 2 \frac{h y}{2} = 2 A$

Rewrite the expression.

$h x + 2 \frac{h y}{2} = 2 A$

$h x + 2 \frac{h y}{2} = 2 A$

Cancel the common factor of $2$ .

Cancel the common factor.

$h x + 2 \frac{h y}{2} = 2 A$

Rewrite the expression.

$h x + h y = 2 A$

$h x + h y = 2 A$

$h x + h y = 2 A$

$h x + h y = 2 A$

Step 4

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

$h x = 2 A - h y$

Step 5

Divide each term in $h x = 2 A - h y$ by $h$ and simplify.

Divide each term in $h x = 2 A - h y$ by $h$ .

$\frac{h x}{h} = \frac{2 A}{h} + \frac{- h y}{h}$

Simplify the left side.

Cancel the common factor of $h$ .

Cancel the common factor.

$\frac{h x}{h} = \frac{2 A}{h} + \frac{- h y}{h}$

Divide $x$ by $1$ .

$x = \frac{2 A}{h} + \frac{- h y}{h}$

$x = \frac{2 A}{h} + \frac{- h y}{h}$

$x = \frac{2 A}{h} + \frac{- h y}{h}$

Simplify the right side.

Simplify each term.

Cancel the common factor of $h$ .

Cancel the common factor.

$x = \frac{2 A}{h} + \frac{- h y}{h}$

Divide $- 1 y$ by $1$ .

$x = \frac{2 A}{h} - 1 y$

$x = \frac{2 A}{h} - 1 y$

Rewrite $- 1 y$ as $- y$ .

$x = \frac{2 A}{h} - y$

$x = \frac{2 A}{h} - y$

$x = \frac{2 A}{h} - y$

$x = \frac{2 A}{h} - y$

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