Pre-Algebra Examples

$6 y = 2 x - 5$

Step 1

Divide each term in $6 y = 2 x - 5$ by $6$ and simplify.

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Step 1.1

Divide each term in $6 y = 2 x - 5$ by $6$ .

$\frac{6 y}{6} = \frac{2 x}{6} + \frac{- 5}{6}$

Step 1.2

Simplify the left side.

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Step 1.2.1

Cancel the common factor of $6$ .

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Step 1.2.1.1

Cancel the common factor.

$\frac{6 y}{6} = \frac{2 x}{6} + \frac{- 5}{6}$

Step 1.2.1.2

Divide $y$ by $1$ .

$y = \frac{2 x}{6} + \frac{- 5}{6}$

Step 1.3

Simplify the right side.

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Step 1.3.1

Simplify each term.

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Step 1.3.1.1

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

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Step 1.3.1.1.1

Factor $2$ out of $2 x$ .

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

Step 1.3.1.1.2

Cancel the common factors.

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Step 1.3.1.1.2.1

Factor $2$ out of $6$ .

$y = \frac{2 x}{2 \cdot 3} + \frac{- 5}{6}$

Step 1.3.1.1.2.2

Cancel the common factor.

$y = \frac{2 x}{2 \cdot 3} + \frac{- 5}{6}$

Step 1.3.1.1.2.3

Rewrite the expression.

$y = \frac{x}{3} + \frac{- 5}{6}$

Step 1.3.1.2

Move the negative in front of the fraction.

$y = \frac{x}{3} - \frac{5}{6}$

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.

$y = \frac{0}{3} - \frac{5}{6}$

Step 3.2

Simplify $\frac{0}{3} - \frac{5}{6}$ .

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Step 3.2.1

Divide $0$ by $3$ .

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

Step 3.2.2

Subtract $\frac{5}{6}$ from $0$ .

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

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.

$y = \frac{1}{3} - \frac{5}{6}$

Step 4.2

Simplify $\frac{1}{3} - \frac{5}{6}$ .

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Step 4.2.1

To write $\frac{1}{3}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$y = \frac{1}{3} \cdot \frac{2}{2} - \frac{5}{6}$

Step 4.2.2

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.2.2.1

Multiply $\frac{1}{3}$ by $\frac{2}{2}$ .

$y = \frac{2}{3 \cdot 2} - \frac{5}{6}$

Step 4.2.2.2

Multiply $3$ by $2$ .

$y = \frac{2}{6} - \frac{5}{6}$

Step 4.2.3

Simplify the expression.

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Step 4.2.3.1

Combine the numerators over the common denominator.

$y = \frac{2 - 5}{6}$

Step 4.2.3.2

Subtract $5$ from $2$ .

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

Step 4.2.4

Cancel the common factor of $- 3$ and $6$ .

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Step 4.2.4.1

Factor $3$ out of $- 3$ .

$y = \frac{3 (- 1)}{6}$

Step 4.2.4.2

Cancel the common factors.

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Step 4.2.4.2.1

Factor $3$ out of $6$ .

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

Step 4.2.4.2.2

Cancel the common factor.

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

Step 4.2.4.2.3

Rewrite the expression.

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

Step 4.2.5

Move the negative in front of the fraction.

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

Step 4.3

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

$(1, - \frac{1}{2})$

Step 5

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

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Step 5.1

Remove parentheses.

$y = \frac{2}{3} - \frac{5}{6}$

Step 5.2

Simplify $\frac{2}{3} - \frac{5}{6}$ .

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Step 5.2.1

To write $\frac{2}{3}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$y = \frac{2}{3} \cdot \frac{2}{2} - \frac{5}{6}$

Step 5.2.2

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

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Step 5.2.2.1

Multiply $\frac{2}{3}$ by $\frac{2}{2}$ .

$y = \frac{2 \cdot 2}{3 \cdot 2} - \frac{5}{6}$

Step 5.2.2.2

Multiply $3$ by $2$ .

$y = \frac{2 \cdot 2}{6} - \frac{5}{6}$

Step 5.2.3

Combine the numerators over the common denominator.

$y = \frac{2 \cdot 2 - 5}{6}$

Step 5.2.4

Simplify the numerator.

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Step 5.2.4.1

Multiply $2$ by $2$ .

$y = \frac{4 - 5}{6}$

Step 5.2.4.2

Subtract $5$ from $4$ .

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

Step 5.2.5

Move the negative in front of the fraction.

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

Step 5.3

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

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

Step 6

These are three possible solutions to the equation.

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

Step 7