Finite Math Examples

$- 8 y + 40 = 32 x$

Step 1

Subtract $40$ from both sides of the equation.

$- 8 y = 32 x - 40$

Step 2

Divide each term in $- 8 y = 32 x - 40$ by $- 8$ and simplify.

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Step 2.1

Divide each term in $- 8 y = 32 x - 40$ by $- 8$ .

$\frac{- 8 y}{- 8} = \frac{32 x}{- 8} + \frac{- 40}{- 8}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $- 8$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{- 8 y}{- 8} = \frac{32 x}{- 8} + \frac{- 40}{- 8}$

Step 2.2.1.2

Divide $y$ by $1$ .

$y = \frac{32 x}{- 8} + \frac{- 40}{- 8}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Simplify each term.

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Step 2.3.1.1

Cancel the common factor of $32$ and $- 8$ .

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Step 2.3.1.1.1

Factor $8$ out of $32 x$ .

$y = \frac{8 (4 x)}{- 8} + \frac{- 40}{- 8}$

Step 2.3.1.1.2

Move the negative one from the denominator of $\frac{4 x}{- 1}$ .

$y = - 1 \cdot (4 x) + \frac{- 40}{- 8}$

Step 2.3.1.2

Rewrite $- 1 \cdot (4 x)$ as $- (4 x)$ .

$y = - (4 x) + \frac{- 40}{- 8}$

Step 2.3.1.3

Multiply $4$ by $- 1$ .

$y = - 4 x + \frac{- 40}{- 8}$

Step 2.3.1.4

Divide $- 40$ by $- 8$ .

$y = - 4 x + 5$

Step 3

Set $- 4 x + 5$ equal to $0$ .

$- 4 x + 5 = 0$

Step 4

Solve for $x$ .

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Step 4.1

Subtract $5$ from both sides of the equation.

$- 4 x = - 5$

Step 4.2

Divide each term in $- 4 x = - 5$ by $- 4$ and simplify.

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Step 4.2.1

Divide each term in $- 4 x = - 5$ by $- 4$ .

$\frac{- 4 x}{- 4} = \frac{- 5}{- 4}$

Step 4.2.2

Simplify the left side.

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Step 4.2.2.1

Cancel the common factor of $- 4$ .

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Step 4.2.2.1.1

Cancel the common factor.

$\frac{- 4 x}{- 4} = \frac{- 5}{- 4}$

Step 4.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 5}{- 4}$

Step 4.2.3

Simplify the right side.

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Step 4.2.3.1

Dividing two negative values results in a positive value.

$x = \frac{5}{4}$

$x = \frac{5}{4}$ (Multiplicity of $1$ )

Step 5