Pre-Algebra Examples

$8 - 4 (x - y) = 2 x + 6$

Step 1

Solve for $y$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$8 - 4 x - 4 (- y) = 2 x + 6$

Step 1.1.2

Multiply $- 1$ by $- 4$ .

$8 - 4 x + 4 y = 2 x + 6$

Step 1.2

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

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Step 1.2.1

Subtract $8$ from both sides of the equation.

$- 4 x + 4 y = 2 x + 6 - 8$

Step 1.2.2

Add $4 x$ to both sides of the equation.

$4 y = 2 x + 6 - 8 + 4 x$

Step 1.2.3

Add $2 x$ and $4 x$ .

$4 y = 6 x + 6 - 8$

Step 1.2.4

Subtract $8$ from $6$ .

$4 y = 6 x - 2$

Step 1.3

Divide each term in $4 y = 6 x - 2$ by $4$ and simplify.

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Step 1.3.1

Divide each term in $4 y = 6 x - 2$ by $4$ .

$\frac{4 y}{4} = \frac{6 x}{4} + \frac{- 2}{4}$

Step 1.3.2

Simplify the left side.

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Step 1.3.2.1

Cancel the common factor of $4$ .

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Step 1.3.2.1.1

Cancel the common factor.

$\frac{4 y}{4} = \frac{6 x}{4} + \frac{- 2}{4}$

Step 1.3.2.1.2

Divide $y$ by $1$ .

$y = \frac{6 x}{4} + \frac{- 2}{4}$

Step 1.3.3

Simplify the right side.

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Step 1.3.3.1

Simplify each term.

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Step 1.3.3.1.1

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

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Step 1.3.3.1.1.1

Factor $2$ out of $6 x$ .

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

Step 1.3.3.1.1.2

Cancel the common factors.

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Step 1.3.3.1.1.2.1

Factor $2$ out of $4$ .

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

Step 1.3.3.1.1.2.2

Cancel the common factor.

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

Step 1.3.3.1.1.2.3

Rewrite the expression.

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

Step 1.3.3.1.2

Cancel the common factor of $- 2$ and $4$ .

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Step 1.3.3.1.2.1

Factor $2$ out of $- 2$ .

$y = \frac{3 x}{2} + \frac{2 (- 1)}{4}$

Step 1.3.3.1.2.2

Cancel the common factors.

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Step 1.3.3.1.2.2.1

Factor $2$ out of $4$ .

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

Step 1.3.3.1.2.2.2

Cancel the common factor.

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

Step 1.3.3.1.2.2.3

Rewrite the expression.

$y = \frac{3 x}{2} + \frac{- 1}{2}$

Step 1.3.3.1.3

Move the negative in front of the fraction.

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

Step 2

Reorder terms.

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

Step 3