Pre-Algebra Examples

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

Step 1

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

Step 2

Multiply both sides by $3$ .

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

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

Multiply $3$ by each element of the matrix.

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

Step 3.1.2

Simplify each element in the matrix.

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Step 3.1.2.1

Apply the distributive property.

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

Step 3.1.2.2

Multiply $3$ by $- 3$ .

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

Step 4

Simplify the right side.

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Step 4.1

Simplify $3 (- \frac{2}{3} \cdot (x + 4))$ .

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Step 4.1.1

Apply the distributive property.

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

Step 4.1.2

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

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

Step 4.1.3

Multiply $- \frac{2}{3} \cdot 4$ .

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Step 4.1.3.1

Multiply $4$ by $- 1$ .

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

Step 4.1.3.2

Combine $- 4$ and $\frac{2}{3}$ .

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

Step 4.1.3.3

Multiply $- 4$ by $2$ .

$(3 y - 9) = 3 (- \frac{x \cdot 2}{3} + \frac{- 8}{3})$

Step 4.1.4

Simplify each term.

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Step 4.1.4.1

Move $2$ to the left of $x$ .

$(3 y - 9) = 3 (- \frac{2 \cdot x}{3} + \frac{- 8}{3})$

Step 4.1.4.2

Move the negative in front of the fraction.

$(3 y - 9) = 3 (- \frac{2 x}{3} - \frac{8}{3})$

Step 4.1.5

Simplify terms.

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Step 4.1.5.1

Apply the distributive property.

$(3 y - 9) = 3 (- \frac{2 x}{3}) + 3 (- \frac{8}{3})$

Step 4.1.5.2

Cancel the common factor of $3$ .

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Step 4.1.5.2.1

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

$(3 y - 9) = 3 \frac{- 2 x}{3} + 3 (- \frac{8}{3})$

Step 4.1.5.2.2

Cancel the common factor.

$(3 y - 9) = 3 \frac{- 2 x}{3} + 3 (- \frac{8}{3})$

Step 4.1.5.2.3

Rewrite the expression.

$(3 y - 9) = - 2 x + 3 (- \frac{8}{3})$

Step 4.1.5.3

Cancel the common factor of $3$ .

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Step 4.1.5.3.1

Move the leading negative in $- \frac{8}{3}$ into the numerator.

$(3 y - 9) = - 2 x + 3 (\frac{- 8}{3})$

Step 4.1.5.3.2

Cancel the common factor.

$(3 y - 9) = - 2 x + 3 (\frac{- 8}{3})$

Step 4.1.5.3.3

Rewrite the expression.

$(3 y - 9) = - 2 x - 8$

Step 5

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

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Step 5.1

Add $2 x$ to both sides of the equation.

$(3 y - 9) + 2 x = - 8$

Step 5.2

Move $- 9$ .

$3 y + 2 x - 9 = - 8$

Step 5.3

Reorder $3 y$ and $2 x$ .

$2 x + 3 y - 9 = - 8$

Step 6

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

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Step 6.1

Add $9$ to both sides of the equation.

$2 x + 3 y = - 8 + 9$

Step 6.2

Add $- 8$ and $9$ .

$2 x + 3 y = 1$

Step 7