Pre-Algebra Examples

$y - 8 = - \frac{1}{2} \cdot (x + 4)$

Step 1

The standard form of a linear equation is $A x + B y = C$ .

Step 2

Multiply both sides by $2$ .

$2 (y - 8) = 2 (- \frac{1}{2} \cdot (x + 4))$

Step 3

Simplify the left side.

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Step 3.1

Simplify $2 (y - 8)$ .

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Step 3.1.1

Apply the distributive property.

$2 y + 2 \cdot - 8 = 2 (- \frac{1}{2} \cdot (x + 4))$

Step 3.1.2

Multiply $2$ by $- 8$ .

$2 y - 16 = 2 (- \frac{1}{2} \cdot (x + 4))$

Step 4

Simplify the right side.

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Step 4.1

Simplify $2 (- \frac{1}{2} \cdot (x + 4))$ .

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Step 4.1.1

Apply the distributive property.

$2 y - 16 = 2 (- \frac{1}{2} x - \frac{1}{2} \cdot 4)$

Step 4.1.2

Combine $x$ and $\frac{1}{2}$ .

$2 y - 16 = 2 (- \frac{x}{2} - \frac{1}{2} \cdot 4)$

Step 4.1.3

Cancel the common factor of $2$ .

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Step 4.1.3.1

Move the leading negative in $- \frac{1}{2}$ into the numerator.

$2 y - 16 = 2 (- \frac{x}{2} + \frac{- 1}{2} \cdot 4)$

Step 4.1.3.2

Factor $2$ out of $4$ .

$2 y - 16 = 2 (- \frac{x}{2} + \frac{- 1}{2} \cdot (2 (2)))$

Step 4.1.3.3

Cancel the common factor.

$2 y - 16 = 2 (- \frac{x}{2} + \frac{- 1}{2} \cdot (2 \cdot 2))$

Step 4.1.3.4

Rewrite the expression.

$2 y - 16 = 2 (- \frac{x}{2} - 1 \cdot 2)$

Step 4.1.4

Multiply $- 1$ by $2$ .

$2 y - 16 = 2 (- \frac{x}{2} - 2)$

Step 4.1.5

Apply the distributive property.

$2 y - 16 = 2 (- \frac{x}{2}) + 2 \cdot - 2$

Step 4.1.6

Cancel the common factor of $2$ .

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Step 4.1.6.1

Move the leading negative in $- \frac{x}{2}$ into the numerator.

$2 y - 16 = 2 \frac{- x}{2} + 2 \cdot - 2$

Step 4.1.6.2

Cancel the common factor.

$2 y - 16 = 2 \frac{- x}{2} + 2 \cdot - 2$

Step 4.1.6.3

Rewrite the expression.

$2 y - 16 = - x + 2 \cdot - 2$

Step 4.1.7

Multiply $2$ by $- 2$ .

$2 y - 16 = - x - 4$

Step 5

Move all terms containing variables to the left side of the equation.

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Step 5.1

Add $x$ to both sides of the equation.

$2 y - 16 + x = - 4$

Step 5.2

Move $- 16$ .

$2 y + x - 16 = - 4$

Step 5.3

Reorder $2 y$ and $x$ .

$x + 2 y - 16 = - 4$

Step 6

Move all terms not containing a variable to the right side of the equation.

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Step 6.1

Add $16$ to both sides of the equation.

$x + 2 y = - 4 + 16$

Step 6.2

Add $- 4$ and $16$ .

$x + 2 y = 12$

Step 7