Finite Math Examples

$y - 5 = - \frac{3}{8} \cdot (x - (3))$

Step 1

Rewrite the equation as $- \frac{3}{8} \cdot (x - (3)) = y - 5$ .

$- \frac{3}{8} \cdot (x - (3)) = y - 5$

Step 2

Multiply both sides of the equation by $- \frac{8}{3}$ .

$- \frac{8}{3} (- \frac{3}{8} \cdot (x - (3))) = - \frac{8}{3} (y - 5)$

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

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Step 3.1.1.1

Multiply $- 1$ by $3$ .

$- \frac{8}{3} (- \frac{3}{8} \cdot (x - 3)) = - \frac{8}{3} (y - 5)$

Step 3.1.1.2

Apply the distributive property.

$- \frac{8}{3} (- \frac{3}{8} x - \frac{3}{8} \cdot - 3) = - \frac{8}{3} (y - 5)$

Step 3.1.1.3

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

$- \frac{8}{3} (- \frac{x \cdot 3}{8} - \frac{3}{8} \cdot - 3) = - \frac{8}{3} (y - 5)$

Step 3.1.1.4

Multiply $- \frac{3}{8} \cdot - 3$ .

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Step 3.1.1.4.1

Multiply $- 3$ by $- 1$ .

$- \frac{8}{3} (- \frac{x \cdot 3}{8} + 3 (\frac{3}{8})) = - \frac{8}{3} (y - 5)$

Step 3.1.1.4.2

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

$- \frac{8}{3} (- \frac{x \cdot 3}{8} + \frac{3 \cdot 3}{8}) = - \frac{8}{3} (y - 5)$

Step 3.1.1.4.3

Multiply $3$ by $3$ .

$- \frac{8}{3} (- \frac{x \cdot 3}{8} + \frac{9}{8}) = - \frac{8}{3} (y - 5)$

Step 3.1.1.5

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

$- \frac{8}{3} (- \frac{3 x}{8} + \frac{9}{8}) = - \frac{8}{3} (y - 5)$

Step 3.1.1.6

Simplify terms.

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Step 3.1.1.6.1

Apply the distributive property.

$- \frac{8}{3} (- \frac{3 x}{8}) - \frac{8}{3} \cdot \frac{9}{8} = - \frac{8}{3} (y - 5)$

Step 3.1.1.6.2

Cancel the common factor of $8$ .

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Step 3.1.1.6.2.1

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

$\frac{- 8}{3} (- \frac{3 x}{8}) - \frac{8}{3} \cdot \frac{9}{8} = - \frac{8}{3} (y - 5)$

Step 3.1.1.6.2.2

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

$\frac{- 8}{3} \cdot \frac{- 3 x}{8} - \frac{8}{3} \cdot \frac{9}{8} = - \frac{8}{3} (y - 5)$

Step 3.1.1.6.2.3

Factor $8$ out of $- 8$ .

$\frac{8 (- 1)}{3} \cdot \frac{- 3 x}{8} - \frac{8}{3} \cdot \frac{9}{8} = - \frac{8}{3} (y - 5)$

Step 3.1.1.6.2.4

Cancel the common factor.

$\frac{8 \cdot - 1}{3} \cdot \frac{- 3 x}{8} - \frac{8}{3} \cdot \frac{9}{8} = - \frac{8}{3} (y - 5)$

Step 3.1.1.6.2.5

Rewrite the expression.

$\frac{- 1}{3} (- 3 x) - \frac{8}{3} \cdot \frac{9}{8} = - \frac{8}{3} (y - 5)$

Step 3.1.1.6.3

Cancel the common factor of $3$ .

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Step 3.1.1.6.3.1

Factor $3$ out of $- 3 x$ .

$\frac{- 1}{3} (3 (- x)) - \frac{8}{3} \cdot \frac{9}{8} = - \frac{8}{3} (y - 5)$

Step 3.1.1.6.3.2

Cancel the common factor.

$\frac{- 1}{3} (3 (- x)) - \frac{8}{3} \cdot \frac{9}{8} = - \frac{8}{3} (y - 5)$

Step 3.1.1.6.3.3

Rewrite the expression.

$- - x - \frac{8}{3} \cdot \frac{9}{8} = - \frac{8}{3} (y - 5)$

Step 3.1.1.6.4

Multiply.

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Step 3.1.1.6.4.1

Multiply $- 1$ by $- 1$ .

$1 x - \frac{8}{3} \cdot \frac{9}{8} = - \frac{8}{3} (y - 5)$

Step 3.1.1.6.4.2

Multiply $x$ by $1$ .

$x - \frac{8}{3} \cdot \frac{9}{8} = - \frac{8}{3} (y - 5)$

Step 3.1.1.6.5

Cancel the common factor of $8$ .

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Step 3.1.1.6.5.1

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

$x + \frac{- 8}{3} \cdot \frac{9}{8} = - \frac{8}{3} (y - 5)$

Step 3.1.1.6.5.2

Factor $8$ out of $- 8$ .

$x + \frac{8 (- 1)}{3} \cdot \frac{9}{8} = - \frac{8}{3} (y - 5)$

Step 3.1.1.6.5.3

Cancel the common factor.

$x + \frac{8 \cdot - 1}{3} \cdot \frac{9}{8} = - \frac{8}{3} (y - 5)$

Step 3.1.1.6.5.4

Rewrite the expression.

$x + \frac{- 1}{3} \cdot 9 = - \frac{8}{3} (y - 5)$

Step 3.1.1.6.6

Cancel the common factor of $3$ .

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Step 3.1.1.6.6.1

Factor $3$ out of $9$ .

$x + \frac{- 1}{3} \cdot (3 (3)) = - \frac{8}{3} (y - 5)$

Step 3.1.1.6.6.2

Cancel the common factor.

$x + \frac{- 1}{3} \cdot (3 \cdot 3) = - \frac{8}{3} (y - 5)$

Step 3.1.1.6.6.3

Rewrite the expression.

$x - 1 \cdot 3 = - \frac{8}{3} (y - 5)$

Step 3.1.1.6.7

Multiply $- 1$ by $3$ .

$x - 3 = - \frac{8}{3} (y - 5)$

Step 3.2

Simplify the right side.

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Step 3.2.1

Simplify $- \frac{8}{3} (y - 5)$ .

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Step 3.2.1.1

Apply the distributive property.

$x - 3 = - \frac{8}{3} y - \frac{8}{3} \cdot - 5$

Step 3.2.1.2

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

$x - 3 = - \frac{y \cdot 8}{3} - \frac{8}{3} \cdot - 5$

Step 3.2.1.3

Multiply $- \frac{8}{3} \cdot - 5$ .

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Step 3.2.1.3.1

Multiply $- 5$ by $- 1$ .

$x - 3 = - \frac{y \cdot 8}{3} + 5 (\frac{8}{3})$

Step 3.2.1.3.2

Combine $5$ and $\frac{8}{3}$ .

$x - 3 = - \frac{y \cdot 8}{3} + \frac{5 \cdot 8}{3}$

Step 3.2.1.3.3

Multiply $5$ by $8$ .

$x - 3 = - \frac{y \cdot 8}{3} + \frac{40}{3}$

Step 3.2.1.4

Move $8$ to the left of $y$ .

$x - 3 = - \frac{8 y}{3} + \frac{40}{3}$

Step 4

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

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Step 4.1

Add $3$ to both sides of the equation.

$x = - \frac{8 y}{3} + \frac{40}{3} + 3$

Step 4.2

To write $3$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$x = - \frac{8 y}{3} + \frac{40}{3} + 3 \cdot \frac{3}{3}$

Step 4.3

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

$x = - \frac{8 y}{3} + \frac{40}{3} + \frac{3 \cdot 3}{3}$

Step 4.4

Combine the numerators over the common denominator.

$x = - \frac{8 y}{3} + \frac{40 + 3 \cdot 3}{3}$

Step 4.5

Simplify the numerator.

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Step 4.5.1

Multiply $3$ by $3$ .

$x = - \frac{8 y}{3} + \frac{40 + 9}{3}$

Step 4.5.2

Add $40$ and $9$ .

$x = - \frac{8 y}{3} + \frac{49}{3}$