Pre-Algebra Examples

$x + 4 y + 4 = 0$

Step 1

Solve the equation for $y$ .

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Step 1.1

Move all terms not containing $y$ to the right side of the equation.

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Step 1.1.1

Subtract $x$ from both sides of the equation.

$4 y + 4 = - x$

Step 1.1.2

Subtract $4$ from both sides of the equation.

$4 y = - x - 4$

Step 1.2

Divide each term in $4 y = - x - 4$ by $4$ and simplify.

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Step 1.2.1

Divide each term in $4 y = - x - 4$ by $4$ .

$\frac{4 y}{4} = \frac{- x}{4} + \frac{- 4}{4}$

Step 1.2.2

Simplify the left side.

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Step 1.2.2.1

Cancel the common factor of $4$ .

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Step 1.2.2.1.1

Cancel the common factor.

$\frac{4 y}{4} = \frac{- x}{4} + \frac{- 4}{4}$

Step 1.2.2.1.2

Divide $y$ by $1$ .

$y = \frac{- x}{4} + \frac{- 4}{4}$

Step 1.2.3

Simplify the right side.

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Step 1.2.3.1

Simplify each term.

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Step 1.2.3.1.1

Move the negative in front of the fraction.

$y = - \frac{x}{4} + \frac{- 4}{4}$

Step 1.2.3.1.2

Divide $- 4$ by $4$ .

$y = - \frac{x}{4} - 1$

Step 2

Choose any value for $x$ that is in the domain to plug into the equation.

Step 3

Choose $0$ to substitute in for $x$ to find the ordered pair.

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Step 3.1

Remove parentheses.

$y = - \frac{0}{4} - 1$

Step 3.2

Simplify $- \frac{0}{4} - 1$ .

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Step 3.2.1

Simplify each term.

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Step 3.2.1.1

Divide $0$ by $4$ .

$y = - 0 - 1$

Step 3.2.1.2

Multiply $- 1$ by $0$ .

$y = 0 - 1$

Step 3.2.2

Subtract $1$ from $0$ .

$y = - 1$

Step 3.3

Use the $x$ and $y$ values to form the ordered pair.

$(0, - 1)$

Step 4

Choose $1$ to substitute in for $x$ to find the ordered pair.

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Step 4.1

Remove parentheses.

$y = - \frac{1}{4} - 1$

Step 4.2

Simplify $- \frac{1}{4} - 1$ .

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Step 4.2.1

To write $- 1$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$y = - \frac{1}{4} - 1 \cdot \frac{4}{4}$

Step 4.2.2

Combine $- 1$ and $\frac{4}{4}$ .

$y = - \frac{1}{4} + \frac{- 1 \cdot 4}{4}$

Step 4.2.3

Combine the numerators over the common denominator.

$y = \frac{- 1 - 1 \cdot 4}{4}$

Step 4.2.4

Simplify the numerator.

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Step 4.2.4.1

Multiply $- 1$ by $4$ .

$y = \frac{- 1 - 4}{4}$

Step 4.2.4.2

Subtract $4$ from $- 1$ .

$y = \frac{- 5}{4}$

Step 4.2.5

Move the negative in front of the fraction.

$y = - \frac{5}{4}$

Step 4.3

Use the $x$ and $y$ values to form the ordered pair.

$(1, - \frac{5}{4})$

Step 5

Choose $2$ to substitute in for $x$ to find the ordered pair.

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Step 5.1

Remove parentheses.

$y = - \frac{2}{4} - 1$

Step 5.2

Simplify $- \frac{2}{4} - 1$ .

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Step 5.2.1

Cancel the common factor of $2$ and $4$ .

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Step 5.2.1.1

Factor $2$ out of $2$ .

$y = - \frac{2 (1)}{4} - 1$

Step 5.2.1.2

Cancel the common factors.

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Step 5.2.1.2.1

Factor $2$ out of $4$ .

$y = - \frac{2 \cdot 1}{2 \cdot 2} - 1$

Step 5.2.1.2.2

Cancel the common factor.

$y = - \frac{2 \cdot 1}{2 \cdot 2} - 1$

Step 5.2.1.2.3

Rewrite the expression.

$y = - \frac{1}{2} - 1$

Step 5.2.2

To write $- 1$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$y = - \frac{1}{2} - 1 \cdot \frac{2}{2}$

Step 5.2.3

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

$y = - \frac{1}{2} + \frac{- 1 \cdot 2}{2}$

Step 5.2.4

Combine the numerators over the common denominator.

$y = \frac{- 1 - 1 \cdot 2}{2}$

Step 5.2.5

Simplify the numerator.

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Step 5.2.5.1

Multiply $- 1$ by $2$ .

$y = \frac{- 1 - 2}{2}$

Step 5.2.5.2

Subtract $2$ from $- 1$ .

$y = \frac{- 3}{2}$

Step 5.2.6

Move the negative in front of the fraction.

$y = - \frac{3}{2}$

Step 5.3

Use the $x$ and $y$ values to form the ordered pair.

$(2, - \frac{3}{2})$

Step 6

These are three possible solutions to the equation.

$(0, - 1), (1, - \frac{5}{4}), (2, - \frac{3}{2})$

Step 7