Finite Math Examples

$y - 8 = \frac{8 - 3}{- 11 - 5} \cdot (x + 11)$

Step 1

Rewrite the equation as $\frac{8 - 3}{- 11 - 5} \cdot (x + 11) = y - 8$ .

$\frac{8 - 3}{- 11 - 5} \cdot (x + 11) = y - 8$

Step 2

Multiply both sides of the equation by $\frac{- 11 - 5}{8 - 3}$ .

$\frac{- 11 - 5}{8 - 3} (\frac{8 - 3}{- 11 - 5} \cdot (x + 11)) = \frac{- 11 - 5}{8 - 3} (y - 8)$

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 $\frac{- 11 - 5}{8 - 3} (\frac{8 - 3}{- 11 - 5} \cdot (x + 11))$ .

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Step 3.1.1.1

Simplify the expression.

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Step 3.1.1.1.1

Subtract $5$ from $- 11$ .

$\frac{- 16}{8 - 3} (\frac{8 - 3}{- 11 - 5} \cdot (x + 11)) = \frac{- 11 - 5}{8 - 3} (y - 8)$

Step 3.1.1.1.2

Subtract $3$ from $8$ .

$\frac{- 16}{5} (\frac{8 - 3}{- 11 - 5} \cdot (x + 11)) = \frac{- 11 - 5}{8 - 3} (y - 8)$

Step 3.1.1.1.3

Move the negative in front of the fraction.

$- \frac{16}{5} (\frac{8 - 3}{- 11 - 5} \cdot (x + 11)) = \frac{- 11 - 5}{8 - 3} (y - 8)$

Step 3.1.1.1.4

Subtract $3$ from $8$ .

$- \frac{16}{5} (\frac{5}{- 11 - 5} \cdot (x + 11)) = \frac{- 11 - 5}{8 - 3} (y - 8)$

Step 3.1.1.1.5

Subtract $5$ from $- 11$ .

$- \frac{16}{5} (\frac{5}{- 16} \cdot (x + 11)) = \frac{- 11 - 5}{8 - 3} (y - 8)$

Step 3.1.1.1.6

Move the negative in front of the fraction.

$- \frac{16}{5} (- \frac{5}{16} \cdot (x + 11)) = \frac{- 11 - 5}{8 - 3} (y - 8)$

Step 3.1.1.2

Apply the distributive property.

$- \frac{16}{5} (- \frac{5}{16} x - \frac{5}{16} \cdot 11) = \frac{- 11 - 5}{8 - 3} (y - 8)$

Step 3.1.1.3

Combine $x$ and $\frac{5}{16}$ .

$- \frac{16}{5} (- \frac{x \cdot 5}{16} - \frac{5}{16} \cdot 11) = \frac{- 11 - 5}{8 - 3} (y - 8)$

Step 3.1.1.4

Multiply $- \frac{5}{16} \cdot 11$ .

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Step 3.1.1.4.1

Multiply $11$ by $- 1$ .

$- \frac{16}{5} (- \frac{x \cdot 5}{16} - 11 (\frac{5}{16})) = \frac{- 11 - 5}{8 - 3} (y - 8)$

Step 3.1.1.4.2

Combine $- 11$ and $\frac{5}{16}$ .

$- \frac{16}{5} (- \frac{x \cdot 5}{16} + \frac{- 11 \cdot 5}{16}) = \frac{- 11 - 5}{8 - 3} (y - 8)$

Step 3.1.1.4.3

Multiply $- 11$ by $5$ .

$- \frac{16}{5} (- \frac{x \cdot 5}{16} + \frac{- 55}{16}) = \frac{- 11 - 5}{8 - 3} (y - 8)$

Step 3.1.1.5

Simplify each term.

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Step 3.1.1.5.1

Move $5$ to the left of $x$ .

$- \frac{16}{5} (- \frac{5 \cdot x}{16} + \frac{- 55}{16}) = \frac{- 11 - 5}{8 - 3} (y - 8)$

Step 3.1.1.5.2

Move the negative in front of the fraction.

$- \frac{16}{5} (- \frac{5 x}{16} - \frac{55}{16}) = \frac{- 11 - 5}{8 - 3} (y - 8)$

Step 3.1.1.6

Simplify terms.

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Step 3.1.1.6.1

Apply the distributive property.

$- \frac{16}{5} (- \frac{5 x}{16}) - \frac{16}{5} (- \frac{55}{16}) = \frac{- 11 - 5}{8 - 3} (y - 8)$

Step 3.1.1.6.2

Cancel the common factor of $16$ .

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Step 3.1.1.6.2.1

Move the leading negative in $- \frac{16}{5}$ into the numerator.

$\frac{- 16}{5} (- \frac{5 x}{16}) - \frac{16}{5} (- \frac{55}{16}) = \frac{- 11 - 5}{8 - 3} (y - 8)$

Step 3.1.1.6.2.2

Move the leading negative in $- \frac{5 x}{16}$ into the numerator.

$\frac{- 16}{5} \cdot \frac{- 5 x}{16} - \frac{16}{5} (- \frac{55}{16}) = \frac{- 11 - 5}{8 - 3} (y - 8)$

Step 3.1.1.6.2.3

Factor $16$ out of $- 16$ .

$\frac{16 (- 1)}{5} \cdot \frac{- 5 x}{16} - \frac{16}{5} (- \frac{55}{16}) = \frac{- 11 - 5}{8 - 3} (y - 8)$

Step 3.1.1.6.2.4

Cancel the common factor.

$\frac{16 \cdot - 1}{5} \cdot \frac{- 5 x}{16} - \frac{16}{5} (- \frac{55}{16}) = \frac{- 11 - 5}{8 - 3} (y - 8)$

Step 3.1.1.6.2.5

Rewrite the expression.

$\frac{- 1}{5} (- 5 x) - \frac{16}{5} (- \frac{55}{16}) = \frac{- 11 - 5}{8 - 3} (y - 8)$

Step 3.1.1.6.3

Cancel the common factor of $5$ .

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Step 3.1.1.6.3.1

Factor $5$ out of $- 5 x$ .

$\frac{- 1}{5} (5 (- x)) - \frac{16}{5} (- \frac{55}{16}) = \frac{- 11 - 5}{8 - 3} (y - 8)$

Step 3.1.1.6.3.2

Cancel the common factor.

$\frac{- 1}{5} (5 (- x)) - \frac{16}{5} (- \frac{55}{16}) = \frac{- 11 - 5}{8 - 3} (y - 8)$

Step 3.1.1.6.3.3

Rewrite the expression.

$- - x - \frac{16}{5} (- \frac{55}{16}) = \frac{- 11 - 5}{8 - 3} (y - 8)$

Step 3.1.1.6.4

Multiply.

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Step 3.1.1.6.4.1

Multiply $- 1$ by $- 1$ .

$1 x - \frac{16}{5} (- \frac{55}{16}) = \frac{- 11 - 5}{8 - 3} (y - 8)$

Step 3.1.1.6.4.2

Multiply $x$ by $1$ .

$x - \frac{16}{5} (- \frac{55}{16}) = \frac{- 11 - 5}{8 - 3} (y - 8)$

Step 3.1.1.6.5

Cancel the common factor of $16$ .

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Step 3.1.1.6.5.1

Move the leading negative in $- \frac{16}{5}$ into the numerator.

$x + \frac{- 16}{5} (- \frac{55}{16}) = \frac{- 11 - 5}{8 - 3} (y - 8)$

Step 3.1.1.6.5.2

Move the leading negative in $- \frac{55}{16}$ into the numerator.

$x + \frac{- 16}{5} \cdot \frac{- 55}{16} = \frac{- 11 - 5}{8 - 3} (y - 8)$

Step 3.1.1.6.5.3

Factor $16$ out of $- 16$ .

$x + \frac{16 (- 1)}{5} \cdot \frac{- 55}{16} = \frac{- 11 - 5}{8 - 3} (y - 8)$

Step 3.1.1.6.5.4

Cancel the common factor.

$x + \frac{16 \cdot - 1}{5} \cdot \frac{- 55}{16} = \frac{- 11 - 5}{8 - 3} (y - 8)$

Step 3.1.1.6.5.5

Rewrite the expression.

$x + \frac{- 1}{5} \cdot - 55 = \frac{- 11 - 5}{8 - 3} (y - 8)$

Step 3.1.1.6.6

Cancel the common factor of $5$ .

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Step 3.1.1.6.6.1

Factor $5$ out of $- 55$ .

$x + \frac{- 1}{5} \cdot (5 (- 11)) = \frac{- 11 - 5}{8 - 3} (y - 8)$

Step 3.1.1.6.6.2

Cancel the common factor.

$x + \frac{- 1}{5} \cdot (5 \cdot - 11) = \frac{- 11 - 5}{8 - 3} (y - 8)$

Step 3.1.1.6.6.3

Rewrite the expression.

$x - - 11 = \frac{- 11 - 5}{8 - 3} (y - 8)$

Step 3.1.1.6.7

Multiply $- 1$ by $- 11$ .

$x + 11 = \frac{- 11 - 5}{8 - 3} (y - 8)$

Step 3.2

Simplify the right side.

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Step 3.2.1

Simplify $\frac{- 11 - 5}{8 - 3} (y - 8)$ .

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Step 3.2.1.1

Simplify the expression.

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Step 3.2.1.1.1

Subtract $5$ from $- 11$ .

$x + 11 = \frac{- 16}{8 - 3} (y - 8)$

Step 3.2.1.1.2

Subtract $3$ from $8$ .

$x + 11 = \frac{- 16}{5} (y - 8)$

Step 3.2.1.1.3

Move the negative in front of the fraction.

$x + 11 = - \frac{16}{5} (y - 8)$

Step 3.2.1.2

Apply the distributive property.

$x + 11 = - \frac{16}{5} y - \frac{16}{5} \cdot - 8$

Step 3.2.1.3

Combine $y$ and $\frac{16}{5}$ .

$x + 11 = - \frac{y \cdot 16}{5} - \frac{16}{5} \cdot - 8$

Step 3.2.1.4

Multiply $- \frac{16}{5} \cdot - 8$ .

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Step 3.2.1.4.1

Multiply $- 8$ by $- 1$ .

$x + 11 = - \frac{y \cdot 16}{5} + 8 (\frac{16}{5})$

Step 3.2.1.4.2

Combine $8$ and $\frac{16}{5}$ .

$x + 11 = - \frac{y \cdot 16}{5} + \frac{8 \cdot 16}{5}$

Step 3.2.1.4.3

Multiply $8$ by $16$ .

$x + 11 = - \frac{y \cdot 16}{5} + \frac{128}{5}$

Step 3.2.1.5

Move $16$ to the left of $y$ .

$x + 11 = - \frac{16 y}{5} + \frac{128}{5}$

Step 4

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

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Step 4.1

Subtract $11$ from both sides of the equation.

$x = - \frac{16 y}{5} + \frac{128}{5} - 11$

Step 4.2

To write $- 11$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$x = - \frac{16 y}{5} + \frac{128}{5} - 11 \cdot \frac{5}{5}$

Step 4.3

Combine $- 11$ and $\frac{5}{5}$ .

$x = - \frac{16 y}{5} + \frac{128}{5} + \frac{- 11 \cdot 5}{5}$

Step 4.4

Combine the numerators over the common denominator.

$x = - \frac{16 y}{5} + \frac{128 - 11 \cdot 5}{5}$

Step 4.5

Simplify the numerator.

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Step 4.5.1

Multiply $- 11$ by $5$ .

$x = - \frac{16 y}{5} + \frac{128 - 55}{5}$

Step 4.5.2

Subtract $55$ from $128$ .

$x = - \frac{16 y}{5} + \frac{73}{5}$