Pre-Algebra Examples

$6 y = 8 x + 6$

Step 1

Rewrite the equation as $8 x + 6 = 6 y$ .

$8 x + 6 = 6 y$

Step 2

Subtract $6$ from both sides of the equation.

$8 x = 6 y - 6$

Step 3

Divide each term in $8 x = 6 y - 6$ by $8$ and simplify.

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Step 3.1

Divide each term in $8 x = 6 y - 6$ by $8$ .

$\frac{8 x}{8} = \frac{6 y}{8} + \frac{- 6}{8}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $8$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{8 x}{8} = \frac{6 y}{8} + \frac{- 6}{8}$

Step 3.2.1.2

Divide $x$ by $1$ .

$x = \frac{6 y}{8} + \frac{- 6}{8}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Simplify each term.

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Step 3.3.1.1

Cancel the common factor of $6$ and $8$ .

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Step 3.3.1.1.1

Factor $2$ out of $6 y$ .

$x = \frac{2 (3 y)}{8} + \frac{- 6}{8}$

Step 3.3.1.1.2

Cancel the common factors.

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Step 3.3.1.1.2.1

Factor $2$ out of $8$ .

$x = \frac{2 (3 y)}{2 (4)} + \frac{- 6}{8}$

Step 3.3.1.1.2.2

Cancel the common factor.

$x = \frac{2 (3 y)}{2 \cdot 4} + \frac{- 6}{8}$

Step 3.3.1.1.2.3

Rewrite the expression.

$x = \frac{3 y}{4} + \frac{- 6}{8}$

Step 3.3.1.2

Cancel the common factor of $- 6$ and $8$ .

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Step 3.3.1.2.1

Factor $2$ out of $- 6$ .

$x = \frac{3 y}{4} + \frac{2 (- 3)}{8}$

Step 3.3.1.2.2

Cancel the common factors.

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Step 3.3.1.2.2.1

Factor $2$ out of $8$ .

$x = \frac{3 y}{4} + \frac{2 \cdot - 3}{2 \cdot 4}$

Step 3.3.1.2.2.2

Cancel the common factor.

$x = \frac{3 y}{4} + \frac{2 \cdot - 3}{2 \cdot 4}$

Step 3.3.1.2.2.3

Rewrite the expression.

$x = \frac{3 y}{4} + \frac{- 3}{4}$

Step 3.3.1.3

Move the negative in front of the fraction.

$x = \frac{3 y}{4} - \frac{3}{4}$