Algebra Examples

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

Step 1

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

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

Step 2

Multiply both sides of the equation by $2$ .

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

Step 3

Simplify the left side.

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Step 3.1

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

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Step 3.1.1

Apply the distributive property.

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

Step 3.1.2

Apply the distributive property.

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

Step 3.1.3

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

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Step 3.1.3.1

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

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

Step 3.1.3.2

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

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

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

Step 3.1.4

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

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Step 3.1.4.1

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

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

Step 3.1.4.2

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

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

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

Step 3.1.5

Apply the distributive property.

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

Step 3.1.6

Cancel the common factor of $2$ .

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Step 3.1.6.1

Cancel the common factor.

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

Step 3.1.6.2

Rewrite the expression.

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

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

Step 3.1.7

Cancel the common factor of $2$ .

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Step 3.1.7.1

Cancel the common factor.

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

Step 3.1.7.2

Rewrite the expression.

$h x + h y = 2 T$

$h x + h y = 2 T$

$h x + h y = 2 T$

$h x + h y = 2 T$

Step 4

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

$h y = 2 T - h x$

Step 5

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

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Step 5.1

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

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

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $h$ .

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Step 5.2.1.1

Cancel the common factor.

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

Step 5.2.1.2

Divide $y$ by $1$ .

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

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

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

Step 5.3

Simplify the right side.

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Step 5.3.1

Simplify each term.

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Step 5.3.1.1

Cancel the common factor of $h$ .

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Step 5.3.1.1.1

Cancel the common factor.

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

Step 5.3.1.1.2

Divide $- 1 x$ by $1$ .

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

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

Step 5.3.1.2

Rewrite $- 1 x$ as $- x$ .

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

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

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

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

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$