Finite Math Examples

$y = \frac{1}{6} \cdot (7 x - 5)$

Step 1

Simplify $\frac{1}{6} \cdot (7 x - 5)$ .

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Step 1.1

Apply the distributive property.

$y = \frac{1}{6} (7 x) + \frac{1}{6} \cdot - 5$

Step 1.2

Multiply $\frac{1}{6} (7 x)$ .

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Step 1.2.1

Combine $7$ and $\frac{1}{6}$ .

$y = \frac{7}{6} x + \frac{1}{6} \cdot - 5$

Step 1.2.2

Combine $\frac{7}{6}$ and $x$ .

$y = \frac{7 x}{6} + \frac{1}{6} \cdot - 5$

Step 1.3

Combine $\frac{1}{6}$ and $- 5$ .

$y = \frac{7 x}{6} + \frac{- 5}{6}$

Step 1.4

Move the negative in front of the fraction.

$y = \frac{7 x}{6} - \frac{5}{6}$

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.

$y = \frac{7 (0)}{6} - \frac{5}{6}$

Step 3.2

Simplify $\frac{7 (0)}{6} - \frac{5}{6}$ .

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Step 3.2.1

Combine the numerators over the common denominator.

$y = \frac{7 (0) - 5}{6}$

Step 3.2.2

Simplify the expression.

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Step 3.2.2.1

Multiply $7$ by $0$ .

$y = \frac{0 - 5}{6}$

Step 3.2.2.2

Subtract $5$ from $0$ .

$y = \frac{- 5}{6}$

Step 3.2.2.3

Move the negative in front of the fraction.

$y = - \frac{5}{6}$

Step 3.3

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

$(0, - \frac{5}{6})$

Step 4

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

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Step 4.1

Remove parentheses.

$y = \frac{7 (1)}{6} - \frac{5}{6}$

Step 4.2

Simplify $\frac{7 (1)}{6} - \frac{5}{6}$ .

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Step 4.2.1

Combine the numerators over the common denominator.

$y = \frac{7 (1) - 5}{6}$

Step 4.2.2

Simplify the expression.

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Step 4.2.2.1

Multiply $7$ by $1$ .

$y = \frac{7 - 5}{6}$

Step 4.2.2.2

Subtract $5$ from $7$ .

$y = \frac{2}{6}$

Step 4.2.3

Cancel the common factor of $2$ and $6$ .

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Step 4.2.3.1

Factor $2$ out of $2$ .

$y = \frac{2 (1)}{6}$

Step 4.2.3.2

Cancel the common factors.

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Step 4.2.3.2.1

Factor $2$ out of $6$ .

$y = \frac{2 \cdot 1}{2 \cdot 3}$

Step 4.2.3.2.2

Cancel the common factor.

$y = \frac{2 \cdot 1}{2 \cdot 3}$

Step 4.2.3.2.3

Rewrite the expression.

$y = \frac{1}{3}$

Step 4.3

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

$(1, \frac{1}{3})$

Step 5

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

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Step 5.1

Remove parentheses.

$y = \frac{7 (2)}{6} - \frac{5}{6}$

Step 5.2

Simplify $\frac{7 (2)}{6} - \frac{5}{6}$ .

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Step 5.2.1

Combine the numerators over the common denominator.

$y = \frac{7 (2) - 5}{6}$

Step 5.2.2

Simplify the expression.

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Step 5.2.2.1

Multiply $7$ by $2$ .

$y = \frac{14 - 5}{6}$

Step 5.2.2.2

Subtract $5$ from $14$ .

$y = \frac{9}{6}$

Step 5.2.3

Cancel the common factor of $9$ and $6$ .

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Step 5.2.3.1

Factor $3$ out of $9$ .

$y = \frac{3 (3)}{6}$

Step 5.2.3.2

Cancel the common factors.

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Step 5.2.3.2.1

Factor $3$ out of $6$ .

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

Step 5.2.3.2.2

Cancel the common factor.

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

Step 5.2.3.2.3

Rewrite the expression.

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

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.

$(0, - \frac{5}{6}), (1, \frac{1}{3}), (2, \frac{3}{2})$

Step 7