Finite Math Examples

$y - 6 = - \frac{3}{8} \cdot (x + 16)$

Step 1

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

Step 2

Multiply both sides by $8$ .

$8 (y - 6) = 8 (- \frac{3}{8} \cdot (x + 16))$

Step 3

Simplify the left side.

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Step 3.1

Simplify $8 (y - 6)$ .

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Step 3.1.1

Apply the distributive property.

$8 y + 8 \cdot - 6 = 8 (- \frac{3}{8} \cdot (x + 16))$

Step 3.1.2

Multiply $8$ by $- 6$ .

$8 y - 48 = 8 (- \frac{3}{8} \cdot (x + 16))$

Step 4

Simplify the right side.

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Step 4.1

Simplify $8 (- \frac{3}{8} \cdot (x + 16))$ .

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Step 4.1.1

Simplify terms.

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Step 4.1.1.1

Apply the distributive property.

$8 y - 48 = 8 (- \frac{3}{8} x - \frac{3}{8} \cdot 16)$

Step 4.1.1.2

Combine $x$ and $\frac{3}{8}$ .

$8 y - 48 = 8 (- \frac{x \cdot 3}{8} - \frac{3}{8} \cdot 16)$

Step 4.1.1.3

Cancel the common factor of $8$ .

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Step 4.1.1.3.1

Move the leading negative in $- \frac{3}{8}$ into the numerator.

$8 y - 48 = 8 (- \frac{x \cdot 3}{8} + \frac{- 3}{8} \cdot 16)$

Step 4.1.1.3.2

Factor $8$ out of $16$ .

$8 y - 48 = 8 (- \frac{x \cdot 3}{8} + \frac{- 3}{8} \cdot (8 (2)))$

Step 4.1.1.3.3

Cancel the common factor.

$8 y - 48 = 8 (- \frac{x \cdot 3}{8} + \frac{- 3}{8} \cdot (8 \cdot 2))$

Step 4.1.1.3.4

Rewrite the expression.

$8 y - 48 = 8 (- \frac{x \cdot 3}{8} - 3 \cdot 2)$

Step 4.1.1.4

Multiply $- 3$ by $2$ .

$8 y - 48 = 8 (- \frac{x \cdot 3}{8} - 6)$

Step 4.1.2

Move $3$ to the left of $x$ .

$8 y - 48 = 8 (- \frac{3 x}{8} - 6)$

Step 4.1.3

Simplify terms.

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Step 4.1.3.1

Apply the distributive property.

$8 y - 48 = 8 (- \frac{3 x}{8}) + 8 \cdot - 6$

Step 4.1.3.2

Cancel the common factor of $8$ .

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Step 4.1.3.2.1

Move the leading negative in $- \frac{3 x}{8}$ into the numerator.

$8 y - 48 = 8 \frac{- 3 x}{8} + 8 \cdot - 6$

Step 4.1.3.2.2

Cancel the common factor.

$8 y - 48 = 8 \frac{- 3 x}{8} + 8 \cdot - 6$

Step 4.1.3.2.3

Rewrite the expression.

$8 y - 48 = - 3 x + 8 \cdot - 6$

Step 4.1.3.3

Multiply $8$ by $- 6$ .

$8 y - 48 = - 3 x - 48$

Step 5

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

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Step 5.1

Add $3 x$ to both sides of the equation.

$8 y - 48 + 3 x = - 48$

Step 5.2

Move $- 48$ .

$8 y + 3 x - 48 = - 48$

Step 5.3

Reorder $8 y$ and $3 x$ .

$3 x + 8 y - 48 = - 48$

Step 6

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

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Step 6.1

Add $48$ to both sides of the equation.

$3 x + 8 y = - 48 + 48$

Step 6.2

Add $- 48$ and $48$ .

$3 x + 8 y = 0$

Step 7