Finite Math Examples

$y - 4 = - \frac{1}{2} \cdot (x + 6)$

Step 1

Rewrite the equation as $- \frac{1}{2} \cdot (x + 6) = y - 4$ .

$- \frac{1}{2} \cdot (x + 6) = y - 4$

Step 2

Multiply both sides of the equation by $- 2$ .

$- 2 (- \frac{1}{2} \cdot (x + 6)) = - 2 (y - 4)$

Step 3

Simplify both sides of the equation.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Simplify $- 2 (- \frac{1}{2} \cdot (x + 6))$ .

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Step 3.1.1.1

Apply the distributive property.

$- 2 (- \frac{1}{2} x - \frac{1}{2} \cdot 6) = - 2 (y - 4)$

Step 3.1.1.2

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

$- 2 (- \frac{x}{2} - \frac{1}{2} \cdot 6) = - 2 (y - 4)$

Step 3.1.1.3

Cancel the common factor of $2$ .

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Step 3.1.1.3.1

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

$- 2 (- \frac{x}{2} + \frac{- 1}{2} \cdot 6) = - 2 (y - 4)$

Step 3.1.1.3.2

Factor $2$ out of $6$ .

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

Step 3.1.1.3.3

Cancel the common factor.

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

Step 3.1.1.3.4

Rewrite the expression.

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

Step 3.1.1.4

Multiply $- 1$ by $3$ .

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

Step 3.1.1.5

Apply the distributive property.

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

Step 3.1.1.6

Cancel the common factor of $2$ .

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Step 3.1.1.6.1

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

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

Step 3.1.1.6.2

Factor $2$ out of $- 2$ .

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

Step 3.1.1.6.3

Cancel the common factor.

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

Step 3.1.1.6.4

Rewrite the expression.

$- - x - 2 \cdot - 3 = - 2 (y - 4)$

Step 3.1.1.7

Multiply.

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Step 3.1.1.7.1

Multiply $- 1$ by $- 1$ .

$1 x - 2 \cdot - 3 = - 2 (y - 4)$

Step 3.1.1.7.2

Multiply $x$ by $1$ .

$x - 2 \cdot - 3 = - 2 (y - 4)$

Step 3.1.1.7.3

Multiply $- 2$ by $- 3$ .

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

Step 3.2

Simplify the right side.

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Step 3.2.1

Simplify $- 2 (y - 4)$ .

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Step 3.2.1.1

Apply the distributive property.

$x + 6 = - 2 y - 2 \cdot - 4$

Step 3.2.1.2

Multiply $- 2$ by $- 4$ .

$x + 6 = - 2 y + 8$

Step 4

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

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Step 4.1

Subtract $6$ from both sides of the equation.

$x = - 2 y + 8 - 6$

Step 4.2

Subtract $6$ from $8$ .

$x = - 2 y + 2$