Finite Math Examples

$- \frac{1}{4} x - \frac{1}{3} y = 12$

Step 1

Simplify each term.

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Step 1.1

Combine $x$ and $\frac{1}{4}$ .

$- \frac{x}{4} - \frac{1}{3} y = 12$

Step 1.2

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

$- \frac{x}{4} - \frac{y}{3} = 12$

$- \frac{x}{4} - \frac{y}{3} = 12$

Step 2

Add $\frac{y}{3}$ to both sides of the equation.

$- \frac{x}{4} = 12 + \frac{y}{3}$

Step 3

Multiply both sides of the equation by $- 4$ .

$- 4 (- \frac{x}{4}) = - 4 (12 + \frac{y}{3})$

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

Simplify $- 4 (- \frac{x}{4})$ .

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Step 4.1.1.1

Cancel the common factor of $4$ .

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Step 4.1.1.1.1

Move the leading negative in $- \frac{x}{4}$ into the numerator.

$- 4 \frac{- x}{4} = - 4 (12 + \frac{y}{3})$

Step 4.1.1.1.2

Factor $4$ out of $- 4$ .

$4 (- 1) \frac{- x}{4} = - 4 (12 + \frac{y}{3})$

Step 4.1.1.1.3

Cancel the common factor.

$4 \cdot - 1 \frac{- x}{4} = - 4 (12 + \frac{y}{3})$

Step 4.1.1.1.4

Rewrite the expression.

$- - x = - 4 (12 + \frac{y}{3})$

$- - x = - 4 (12 + \frac{y}{3})$

Step 4.1.1.2

Multiply.

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Step 4.1.1.2.1

Multiply $- 1$ by $- 1$ .

$1 x = - 4 (12 + \frac{y}{3})$

Step 4.1.1.2.2

Multiply $x$ by $1$ .

$x = - 4 (12 + \frac{y}{3})$

$x = - 4 (12 + \frac{y}{3})$

$x = - 4 (12 + \frac{y}{3})$

$x = - 4 (12 + \frac{y}{3})$

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify $- 4 (12 + \frac{y}{3})$ .

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Step 4.2.1.1

Apply the distributive property.

$x = - 4 \cdot 12 - 4 \frac{y}{3}$

Step 4.2.1.2

Multiply $- 4$ by $12$ .

$x = - 48 - 4 \frac{y}{3}$

Step 4.2.1.3

Combine $- 4$ and $\frac{y}{3}$ .

$x = - 48 + \frac{- 4 y}{3}$

Step 4.2.1.4

Move the negative in front of the fraction.

$x = - 48 - \frac{4 y}{3}$

$x = - 48 - \frac{4 y}{3}$

$x = - 48 - \frac{4 y}{3}$

$x = - 48 - \frac{4 y}{3}$

Step 5

Reorder $- 48$ and $- \frac{4 y}{3}$ .

$x = - \frac{4 y}{3} - 48$

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