Pre-Algebra Examples

$y - 3 = \frac{2}{3} \cdot (x + 6)$

Step 1

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

Step 2

Multiply both sides by $3$ .

$3 (y - 3) = 3 (\frac{2}{3} \cdot (x + 6))$

Step 3

Simplify the left side.

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Step 3.1

Simplify $3 (y - 3)$ .

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Step 3.1.1

Apply the distributive property.

$3 y + 3 \cdot - 3 = 3 (\frac{2}{3} \cdot (x + 6))$

Step 3.1.2

Multiply $3$ by $- 3$ .

$3 y - 9 = 3 (\frac{2}{3} \cdot (x + 6))$

Step 4

Simplify the right side.

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Step 4.1

Simplify $3 (\frac{2}{3} \cdot (x + 6))$ .

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Step 4.1.1

Apply the distributive property.

$3 y - 9 = 3 (\frac{2}{3} x + \frac{2}{3} \cdot 6)$

Step 4.1.2

Combine $\frac{2}{3}$ and $x$ .

$3 y - 9 = 3 (\frac{2 x}{3} + \frac{2}{3} \cdot 6)$

Step 4.1.3

Cancel the common factor of $3$ .

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Step 4.1.3.1

Factor $3$ out of $6$ .

$3 y - 9 = 3 (\frac{2 x}{3} + \frac{2}{3} \cdot (3 (2)))$

Step 4.1.3.2

Cancel the common factor.

$3 y - 9 = 3 (\frac{2 x}{3} + \frac{2}{3} \cdot (3 \cdot 2))$

Step 4.1.3.3

Rewrite the expression.

$3 y - 9 = 3 (\frac{2 x}{3} + 2 \cdot 2)$

Step 4.1.4

Multiply $2$ by $2$ .

$3 y - 9 = 3 (\frac{2 x}{3} + 4)$

Step 4.1.5

Apply the distributive property.

$3 y - 9 = 3 \frac{2 x}{3} + 3 \cdot 4$

Step 4.1.6

Cancel the common factor of $3$ .

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Step 4.1.6.1

Cancel the common factor.

$3 y - 9 = 3 \frac{2 x}{3} + 3 \cdot 4$

Step 4.1.6.2

Rewrite the expression.

$3 y - 9 = 2 x + 3 \cdot 4$

Step 4.1.7

Multiply $3$ by $4$ .

$3 y - 9 = 2 x + 12$

Step 5

Rewrite the equation.

$2 x + 12 = 3 y - 9$

Step 6

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

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Step 6.1

Subtract $3 y$ from both sides of the equation.

$2 x + 12 - 3 y = - 9$

Step 6.2

Move $12$ .

$2 x - 3 y + 12 = - 9$

Step 7

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

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Step 7.1

Subtract $12$ from both sides of the equation.

$2 x - 3 y = - 9 - 12$

Step 7.2

Subtract $12$ from $- 9$ .

$2 x - 3 y = - 21$

Step 8