Finite Math Examples

$\frac{1}{2} x + \frac{1}{3} y = 12$

Step 1

Simplify each term.

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Step 1.1

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

$\frac{x}{2} + \frac{1}{3} y = 12$

Step 1.2

Combine $\frac{1}{3}$ and $y$ .

$\frac{x}{2} + \frac{y}{3} = 12$

$\frac{x}{2} + \frac{y}{3} = 12$

Step 2

Subtract $\frac{y}{3}$ from both sides of the equation.

$\frac{x}{2} = 12 - \frac{y}{3}$

Step 3

Multiply both sides of the equation by $2$ .

$2 \frac{x}{2} = 2 (12 - \frac{y}{3})$

Step 4

Simplify both sides of the equation.

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Step 4.1

Simplify the left side.

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Step 4.1.1

Cancel the common factor of $2$ .

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Step 4.1.1.1

Cancel the common factor.

$2 \frac{x}{2} = 2 (12 - \frac{y}{3})$

Step 4.1.1.2

Rewrite the expression.

$x = 2 (12 - \frac{y}{3})$

$x = 2 (12 - \frac{y}{3})$

$x = 2 (12 - \frac{y}{3})$

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify $2 (12 - \frac{y}{3})$ .

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Step 4.2.1.1

Apply the distributive property.

$x = 2 \cdot 12 + 2 (- \frac{y}{3})$

Step 4.2.1.2

Multiply $2$ by $12$ .

$x = 24 + 2 (- \frac{y}{3})$

Step 4.2.1.3

Multiply $2 (- \frac{y}{3})$ .

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Step 4.2.1.3.1

Multiply $- 1$ by $2$ .

$x = 24 - 2 \frac{y}{3}$

Step 4.2.1.3.2

Combine $- 2$ and $\frac{y}{3}$ .

$x = 24 + \frac{- 2 y}{3}$

$x = 24 + \frac{- 2 y}{3}$

Step 4.2.1.4

Move the negative in front of the fraction.

$x = 24 - \frac{2 y}{3}$

$x = 24 - \frac{2 y}{3}$

$x = 24 - \frac{2 y}{3}$

$x = 24 - \frac{2 y}{3}$

Step 5

Reorder $24$ and $- \frac{2 y}{3}$ .

$x = - \frac{2 y}{3} + 24$

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