Algebra Examples

$y = - \frac{11}{12} x - 2 \frac{5}{6}$

Step 1

The standard form of a linear equation is $A x + B y = C$ .

Step 2

Multiply both sides by $12$ .

$12 y = 12 (- \frac{11}{12} x - 2 \frac{5}{6})$

Step 3

Simplify the right side.

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Step 3.1

Simplify $12 (- \frac{11}{12} x - 2 \frac{5}{6})$ .

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Step 3.1.1

Convert $2 \frac{5}{6}$ to an improper fraction.

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Step 3.1.1.1

A mixed number is an addition of its whole and fractional parts.

$12 y = 12 (- \frac{11}{12} x - (2 + \frac{5}{6}))$

Step 3.1.1.2

Add $2$ and $\frac{5}{6}$ .

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Step 3.1.1.2.1

To write $2$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

$12 y = 12 (- \frac{11}{12} x - (2 \cdot \frac{6}{6} + \frac{5}{6}))$

Step 3.1.1.2.2

Combine $2$ and $\frac{6}{6}$ .

$12 y = 12 (- \frac{11}{12} x - (\frac{2 \cdot 6}{6} + \frac{5}{6}))$

Step 3.1.1.2.3

Combine the numerators over the common denominator.

$12 y = 12 (- \frac{11}{12} x - \frac{2 \cdot 6 + 5}{6})$

Step 3.1.1.2.4

Simplify the numerator.

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Step 3.1.1.2.4.1

Multiply $2$ by $6$ .

$12 y = 12 (- \frac{11}{12} x - \frac{12 + 5}{6})$

Step 3.1.1.2.4.2

Add $12$ and $5$ .

$12 y = 12 (- \frac{11}{12} x - \frac{17}{6})$

Step 3.1.2

Simplify each term.

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Step 3.1.2.1

Combine $x$ and $\frac{11}{12}$ .

$12 y = 12 (- \frac{x \cdot 11}{12} - \frac{17}{6})$

Step 3.1.2.2

Move $11$ to the left of $x$ .

$12 y = 12 (- \frac{11 x}{12} - \frac{17}{6})$

Step 3.1.3

Simplify terms.

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Step 3.1.3.1

Apply the distributive property.

$12 y = 12 (- \frac{11 x}{12}) + 12 (- \frac{17}{6})$

Step 3.1.3.2

Cancel the common factor of $12$ .

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Step 3.1.3.2.1

Move the leading negative in $- \frac{11 x}{12}$ into the numerator.

$12 y = 12 \frac{- 11 x}{12} + 12 (- \frac{17}{6})$

Step 3.1.3.2.2

Cancel the common factor.

$12 y = 12 \frac{- 11 x}{12} + 12 (- \frac{17}{6})$

Step 3.1.3.2.3

Rewrite the expression.

$12 y = - 11 x + 12 (- \frac{17}{6})$

Step 3.1.3.3

Cancel the common factor of $6$ .

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Step 3.1.3.3.1

Move the leading negative in $- \frac{17}{6}$ into the numerator.

$12 y = - 11 x + 12 (\frac{- 17}{6})$

Step 3.1.3.3.2

Factor $6$ out of $12$ .

$12 y = - 11 x + 6 (2) \frac{- 17}{6}$

Step 3.1.3.3.3

Cancel the common factor.

$12 y = - 11 x + 6 \cdot 2 \frac{- 17}{6}$

Step 3.1.3.3.4

Rewrite the expression.

$12 y = - 11 x + 2 \cdot - 17$

Step 3.1.3.4

Multiply $2$ by $- 17$ .

$12 y = - 11 x - 34$

Step 4

Move all terms containing variables to the left side of the equation.

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Step 4.1

Add $11 x$ to both sides of the equation.

$12 y + 11 x = - 34$

Step 4.2

Reorder $12 y$ and $11 x$ .

$11 x + 12 y = - 34$

Step 5