Finite Math Examples

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

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

Step 1

The standard form of a linear equation is

A x + B y = C

$A x + B y = C$ .

Step 2

Multiply both sides by

3

$3$ .

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

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

Step 3

Simplify the left side.

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Step 3.1

Simplify

3 (y - (- 3))

$3 (y - (- 3))$ .

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Step 3.1.1

Multiply

- 1

$- 1$ by

- 3

$- 3$ .

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

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

Step 3.1.2

Apply the distributive property.

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

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

Step 3.1.3

Multiply

3

$3$ by

3

$3$ .

3 y + 9 = 3 (\frac{- 1}{3} \cdot (x + 3))

$3 y + 9 = 3 (\frac{- 1}{3} \cdot (x + 3))$

3 y + 9 = 3 (\frac{- 1}{3} \cdot (x + 3))

$3 y + 9 = 3 (\frac{- 1}{3} \cdot (x + 3))$

3 y + 9 = 3 (\frac{- 1}{3} \cdot (x + 3))

$3 y + 9 = 3 (\frac{- 1}{3} \cdot (x + 3))$

Step 4

Simplify the right side.

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Step 4.1

Simplify

3 (\frac{- 1}{3} \cdot (x + 3))

$3 (\frac{- 1}{3} \cdot (x + 3))$ .

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Step 4.1.1

Move the negative in front of the fraction.

3 y + 9 = 3 (- \frac{1}{3} \cdot (x + 3))

$3 y + 9 = 3 (- \frac{1}{3} \cdot (x + 3))$

Step 4.1.2

Apply the distributive property.

3 y + 9 = 3 (- \frac{1}{3} x - \frac{1}{3} \cdot 3)

$3 y + 9 = 3 (- \frac{1}{3} x - \frac{1}{3} \cdot 3)$

Step 4.1.3

Combine

x

$x$ and

\frac{1}{3}

$\frac{1}{3}$ .

3 y + 9 = 3 (- \frac{x}{3} - \frac{1}{3} \cdot 3)

$3 y + 9 = 3 (- \frac{x}{3} - \frac{1}{3} \cdot 3)$

Step 4.1.4

Cancel the common factor of

3

$3$ .

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Step 4.1.4.1

Move the leading negative in

- \frac{1}{3}

$- \frac{1}{3}$ into the numerator.

3 y + 9 = 3 (- \frac{x}{3} + \frac{- 1}{3} \cdot 3)

$3 y + 9 = 3 (- \frac{x}{3} + \frac{- 1}{3} \cdot 3)$

Step 4.1.4.2

Cancel the common factor.

$3 y + 9 = 3 (- \frac{x}{3} + \frac{- 1}{3} \cdot 3)$

Step 4.1.4.3

Rewrite the expression.

$3 y + 9 = 3 (- \frac{x}{3} - 1)$

Step 4.1.5

Apply the distributive property.

$3 y + 9 = 3 (- \frac{x}{3}) + 3 \cdot - 1$

Step 4.1.6

Cancel the common factor of

$3$ .

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Step 4.1.6.1

Move the leading negative in

$- \frac{x}{3}$ into the numerator.

$3 y + 9 = 3 \frac{- x}{3} + 3 \cdot - 1$

Step 4.1.6.2

Cancel the common factor.

$3 y + 9 = 3 \frac{- x}{3} + 3 \cdot - 1$

Step 4.1.6.3

Rewrite the expression.

$3 y + 9 = - x + 3 \cdot - 1$

Step 4.1.7

Multiply

$3$ by

$- 1$ .

$3 y + 9 = - x - 3$

Step 5

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

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Step 5.1

Add

$x$ to both sides of the equation.

$3 y + 9 + x = - 3$

Step 5.2

Move

$9$ .

$3 y + x + 9 = - 3$

Step 5.3

Reorder

$3 y$ and

$x$ .

$x + 3 y + 9 = - 3$

Step 6

Move all terms not containing a variable to the right side of the equation.

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Step 6.1

Subtract

$9$ from both sides of the equation.

$x + 3 y = - 3 - 9$

Step 6.2

Subtract

$9$ from

$- 3$ .

$x + 3 y = - 12$

Step 7