Pre-Algebra Examples

$y - 1 = - \frac{1}{3} \cdot (x + 2)$

Step 1

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

Step 2

Multiply both sides by $3$ .

$3 (y - 1) = 3 (- \frac{1}{3} \cdot (x + 2))$

Step 3

Simplify the left side.

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Step 3.1

Simplify $3 (y - 1)$ .

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Step 3.1.1

Apply the distributive property.

$3 y + 3 \cdot - 1 = 3 (- \frac{1}{3} \cdot (x + 2))$

Step 3.1.2

Multiply $3$ by $- 1$ .

$3 y - 3 = 3 (- \frac{1}{3} \cdot (x + 2))$

Step 4

Simplify the right side.

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Step 4.1

Simplify $3 (- \frac{1}{3} \cdot (x + 2))$ .

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Step 4.1.1

Apply the distributive property.

$3 y - 3 = 3 (- \frac{1}{3} x - \frac{1}{3} \cdot 2)$

Step 4.1.2

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

$3 y - 3 = 3 (- \frac{x}{3} - \frac{1}{3} \cdot 2)$

Step 4.1.3

Multiply $- \frac{1}{3} \cdot 2$ .

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Step 4.1.3.1

Multiply $2$ by $- 1$ .

$3 y - 3 = 3 (- \frac{x}{3} - 2 (\frac{1}{3}))$

Step 4.1.3.2

Combine $- 2$ and $\frac{1}{3}$ .

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

Step 4.1.4

Move the negative in front of the fraction.

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

Step 4.1.5

Apply the distributive property.

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

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.

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

Step 4.1.6.2

Cancel the common factor.

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

Step 4.1.6.3

Rewrite the expression.

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

Step 4.1.7

Cancel the common factor of $3$ .

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Step 4.1.7.1

Move the leading negative in $- \frac{2}{3}$ into the numerator.

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

Step 4.1.7.2

Cancel the common factor.

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

Step 4.1.7.3

Rewrite the expression.

$3 y - 3 = - x - 2$

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.

$3 y - 3 + x = - 2$

Step 5.2

Move $- 3$ .

$3 y + x - 3 = - 2$

Step 5.3

Reorder $3 y$ and $x$ .

$x + 3 y - 3 = - 2$

Step 6

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

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Step 6.1

Add $3$ to both sides of the equation.

$x + 3 y = - 2 + 3$

Step 6.2

Add $- 2$ and $3$ .

$x + 3 y = 1$

Step 7