Pre-Algebra Examples

$y - 6 = \frac{17}{14} \cdot (x - 6)$

Step 1

Solve the equation for $y$ .

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Step 1.1

Simplify $\frac{17}{14} \cdot (x - 6)$ .

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Step 1.1.1

Rewrite.

$y - 6 = 0 + 0 + \frac{17}{14} \cdot (x - 6)$

Step 1.1.2

Simplify by adding zeros.

$y - 6 = \frac{17}{14} \cdot (x - 6)$

Step 1.1.3

Apply the distributive property.

$y - 6 = \frac{17}{14} x + \frac{17}{14} \cdot - 6$

Step 1.1.4

Combine $\frac{17}{14}$ and $x$ .

$y - 6 = \frac{17 x}{14} + \frac{17}{14} \cdot - 6$

Step 1.1.5

Cancel the common factor of $2$ .

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Step 1.1.5.1

Factor $2$ out of $14$ .

$y - 6 = \frac{17 x}{14} + \frac{17}{2 (7)} \cdot - 6$

Step 1.1.5.2

Factor $2$ out of $- 6$ .

$y - 6 = \frac{17 x}{14} + \frac{17}{2 \cdot 7} \cdot (2 \cdot - 3)$

Step 1.1.5.3

Cancel the common factor.

$y - 6 = \frac{17 x}{14} + \frac{17}{2 \cdot 7} \cdot (2 \cdot - 3)$

Step 1.1.5.4

Rewrite the expression.

$y - 6 = \frac{17 x}{14} + \frac{17}{7} \cdot - 3$

Step 1.1.6

Combine $\frac{17}{7}$ and $- 3$ .

$y - 6 = \frac{17 x}{14} + \frac{17 \cdot - 3}{7}$

Step 1.1.7

Simplify the expression.

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Step 1.1.7.1

Multiply $17$ by $- 3$ .

$y - 6 = \frac{17 x}{14} + \frac{- 51}{7}$

Step 1.1.7.2

Move the negative in front of the fraction.

$y - 6 = \frac{17 x}{14} - \frac{51}{7}$

Step 1.2

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

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Step 1.2.1

Add $6$ to both sides of the equation.

$y = \frac{17 x}{14} - \frac{51}{7} + 6$

Step 1.2.2

To write $6$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$y = \frac{17 x}{14} - \frac{51}{7} + 6 \cdot \frac{7}{7}$

Step 1.2.3

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

$y = \frac{17 x}{14} - \frac{51}{7} + \frac{6 \cdot 7}{7}$

Step 1.2.4

Combine the numerators over the common denominator.

$y = \frac{17 x}{14} + \frac{- 51 + 6 \cdot 7}{7}$

Step 1.2.5

Simplify the numerator.

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Step 1.2.5.1

Multiply $6$ by $7$ .

$y = \frac{17 x}{14} + \frac{- 51 + 42}{7}$

Step 1.2.5.2

Add $- 51$ and $42$ .

$y = \frac{17 x}{14} + \frac{- 9}{7}$

Step 1.2.6

Move the negative in front of the fraction.

$y = \frac{17 x}{14} - \frac{9}{7}$

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.

$y = \frac{17 (0)}{14} - \frac{9}{7}$

Step 3.2

Simplify $\frac{17 (0)}{14} - \frac{9}{7}$ .

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Step 3.2.1

Multiply $17$ by $0$ .

$y = \frac{0}{14} - \frac{9}{7}$

Step 3.2.2

Divide $0$ by $14$ .

$y = 0 - \frac{9}{7}$

Step 3.2.3

Subtract $\frac{9}{7}$ from $0$ .

$y = - \frac{9}{7}$

Step 3.3

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

$(0, - \frac{9}{7})$

Step 4

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

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Step 4.1

Remove parentheses.

$y = \frac{17 (1)}{14} - \frac{9}{7}$

Step 4.2

Simplify $\frac{17 (1)}{14} - \frac{9}{7}$ .

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Step 4.2.1

Multiply $17$ by $1$ .

$y = \frac{17}{14} - \frac{9}{7}$

Step 4.2.2

To write $- \frac{9}{7}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$y = \frac{17}{14} - \frac{9}{7} \cdot \frac{2}{2}$

Step 4.2.3

Write each expression with a common denominator of $14$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.2.3.1

Multiply $\frac{9}{7}$ by $\frac{2}{2}$ .

$y = \frac{17}{14} - \frac{9 \cdot 2}{7 \cdot 2}$

Step 4.2.3.2

Multiply $7$ by $2$ .

$y = \frac{17}{14} - \frac{9 \cdot 2}{14}$

Step 4.2.4

Combine the numerators over the common denominator.

$y = \frac{17 - 9 \cdot 2}{14}$

Step 4.2.5

Simplify the numerator.

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Step 4.2.5.1

Multiply $- 9$ by $2$ .

$y = \frac{17 - 18}{14}$

Step 4.2.5.2

Subtract $18$ from $17$ .

$y = \frac{- 1}{14}$

Step 4.2.6

Move the negative in front of the fraction.

$y = - \frac{1}{14}$

Step 4.3

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

$(1, - \frac{1}{14})$

Step 5

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

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Step 5.1

Remove parentheses.

$y = \frac{17 (2)}{14} - \frac{9}{7}$

Step 5.2

Simplify $\frac{17 (2)}{14} - \frac{9}{7}$ .

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Step 5.2.1

Multiply $17$ by $2$ .

$y = \frac{34}{14} - \frac{9}{7}$

Step 5.2.2

Cancel the common factor of $34$ and $14$ .

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Step 5.2.2.1

Factor $2$ out of $34$ .

$y = \frac{2 (17)}{14} - \frac{9}{7}$

Step 5.2.2.2

Cancel the common factors.

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Step 5.2.2.2.1

Factor $2$ out of $14$ .

$y = \frac{2 \cdot 17}{2 \cdot 7} - \frac{9}{7}$

Step 5.2.2.2.2

Cancel the common factor.

$y = \frac{2 \cdot 17}{2 \cdot 7} - \frac{9}{7}$

Step 5.2.2.2.3

Rewrite the expression.

$y = \frac{17}{7} - \frac{9}{7}$

Step 5.2.3

Combine the numerators over the common denominator.

$y = \frac{17 - 9}{7}$

Step 5.2.4

Subtract $9$ from $17$ .

$y = \frac{8}{7}$

Step 5.3

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

$(2, \frac{8}{7})$

Step 6

These are three possible solutions to the equation.

$(0, - \frac{9}{7}), (1, - \frac{1}{14}), (2, \frac{8}{7})$

Step 7