Algebra Examples

$f (x) = \frac{- x - 10}{x + 6}$

Step 1

Write $f (x) = \frac{- x - 10}{x + 6}$ as an equation.

$y = \frac{- x - 10}{x + 6}$

Step 2

Simplify $\frac{- x - 10}{x + 6}$ .

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Step 2.1

Factor $- 1$ out of $- x$ .

$y = \frac{- (x) - 10}{x + 6}$

Step 2.2

Rewrite $- 10$ as $- 1 (10)$ .

$y = \frac{- (x) - 1 (10)}{x + 6}$

Step 2.3

Factor $- 1$ out of $- (x) - 1 (10)$ .

$y = \frac{- (x + 10)}{x + 6}$

Step 2.4

Simplify the expression.

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Step 2.4.1

Rewrite $- (x + 10)$ as $- 1 (x + 10)$ .

$y = \frac{- 1 (x + 10)}{x + 6}$

Step 2.4.2

Move the negative in front of the fraction.

$y = - \frac{x + 10}{x + 6}$

Step 3

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

Step 4

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

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Step 4.1

Remove parentheses.

$y = - \frac{0 + 10}{(0) + 6}$

Step 4.2

Remove parentheses.

$y = - \frac{0 + 10}{0 + 6}$

Step 4.3

Remove parentheses.

$y = - \frac{(0) + 10}{(0) + 6}$

Step 4.4

Simplify $- \frac{(0) + 10}{(0) + 6}$ .

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Step 4.4.1

Cancel the common factor of $(0) + 10$ and $(0) + 6$ .

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Step 4.4.1.1

Factor $2$ out of $0$ .

$y = - \frac{2 (0) + 10}{(0) + 6}$

Step 4.4.1.2

Factor $2$ out of $10$ .

$y = - \frac{2 \cdot 0 + 2 \cdot 5}{(0) + 6}$

Step 4.4.1.3

Factor $2$ out of $2 \cdot 0 + 2 \cdot 5$ .

$y = - \frac{2 \cdot (0 + 5)}{(0) + 6}$

Step 4.4.1.4

Cancel the common factors.

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Step 4.4.1.4.1

Factor $2$ out of $0$ .

$y = - \frac{2 \cdot (0 + 5)}{2 (0) + 6}$

Step 4.4.1.4.2

Factor $2$ out of $6$ .

$y = - \frac{2 \cdot (0 + 5)}{2 \cdot 0 + 2 \cdot 3}$

Step 4.4.1.4.3

Factor $2$ out of $2 \cdot 0 + 2 \cdot 3$ .

$y = - \frac{2 \cdot (0 + 5)}{2 \cdot (0 + 3)}$

Step 4.4.1.4.4

Cancel the common factor.

$y = - \frac{2 \cdot (0 + 5)}{2 \cdot (0 + 3)}$

Step 4.4.1.4.5

Rewrite the expression.

$y = - \frac{0 + 5}{0 + 3}$

Step 4.4.2

Simplify by adding zeros.

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Step 4.4.2.1

Add $0$ and $5$ .

$y = - \frac{5}{0 + 3}$

Step 4.4.2.2

Add $0$ and $3$ .

$y = - \frac{5}{3}$

Step 4.5

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

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

Step 5

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

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Step 5.1

Remove parentheses.

$y = - \frac{1 + 10}{(1) + 6}$

Step 5.2

Remove parentheses.

$y = - \frac{1 + 10}{1 + 6}$

Step 5.3

Remove parentheses.

$y = - \frac{(1) + 10}{(1) + 6}$

Step 5.4

Simplify $- \frac{(1) + 10}{(1) + 6}$ .

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Step 5.4.1

Add $1$ and $10$ .

$y = - \frac{11}{1 + 6}$

Step 5.4.2

Add $1$ and $6$ .

$y = - \frac{11}{7}$

Step 5.5

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

$(1, - \frac{11}{7})$

Step 6

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

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Step 6.1

Remove parentheses.

$y = - \frac{2 + 10}{(2) + 6}$

Step 6.2

Remove parentheses.

$y = - \frac{2 + 10}{2 + 6}$

Step 6.3

Remove parentheses.

$y = - \frac{(2) + 10}{(2) + 6}$

Step 6.4

Simplify $- \frac{(2) + 10}{(2) + 6}$ .

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Step 6.4.1

Cancel the common factor of $(2) + 10$ and $(2) + 6$ .

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Step 6.4.1.1

Factor $2$ out of $2$ .

$y = - \frac{2 \cdot 1 + 10}{2 + 6}$

Step 6.4.1.2

Factor $2$ out of $10$ .

$y = - \frac{2 \cdot 1 + 2 \cdot 5}{(2) + 6}$

Step 6.4.1.3

Factor $2$ out of $2 \cdot 1 + 2 \cdot 5$ .

$y = - \frac{2 \cdot (1 + 5)}{(2) + 6}$

Step 6.4.1.4

Cancel the common factors.

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Step 6.4.1.4.1

Factor $2$ out of $2$ .

$y = - \frac{2 \cdot (1 + 5)}{2 (1) + 6}$

Step 6.4.1.4.2

Factor $2$ out of $6$ .

$y = - \frac{2 \cdot (1 + 5)}{2 \cdot 1 + 2 \cdot 3}$

Step 6.4.1.4.3

Factor $2$ out of $2 \cdot 1 + 2 \cdot 3$ .

$y = - \frac{2 \cdot (1 + 5)}{2 \cdot (1 + 3)}$

Step 6.4.1.4.4

Cancel the common factor.

$y = - \frac{2 \cdot (1 + 5)}{2 \cdot (1 + 3)}$

Step 6.4.1.4.5

Rewrite the expression.

$y = - \frac{1 + 5}{1 + 3}$

Step 6.4.2

Simplify by adding numbers.

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Step 6.4.2.1

Add $1$ and $5$ .

$y = - \frac{6}{1 + 3}$

Step 6.4.2.2

Add $1$ and $3$ .

$y = - \frac{6}{4}$

Step 6.4.3

Cancel the common factor of $6$ and $4$ .

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Step 6.4.3.1

Factor $2$ out of $6$ .

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

Step 6.4.3.2

Cancel the common factors.

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Step 6.4.3.2.1

Factor $2$ out of $4$ .

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

Step 6.4.3.2.2

Cancel the common factor.

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

Step 6.4.3.2.3

Rewrite the expression.

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

Step 6.5

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

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

Step 7

These are three possible solutions to the equation.

$(0, - \frac{5}{3}), (1, - \frac{11}{7}), (2, - \frac{3}{2})$

Step 8