Finite Math Examples

$s = 7 l w + 7 w h + 8 h l$

Step 1

Rewrite the equation as $7 l w + 7 w h + 8 h l = s$ .

$7 l w + 7 w h + 8 h l = s$

Step 2

Subtract $7 l w$ from both sides of the equation.

$7 w h + 8 h l = s - 7 l w$

Step 3

Factor $h$ out of $7 w h + 8 h l$ .

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Step 3.1

Factor $h$ out of $7 w h$ .

$h (7 w) + 8 h l = s - 7 l w$

Step 3.2

Factor $h$ out of $8 h l$ .

$h (7 w) + h (8 l) = s - 7 l w$

Step 3.3

Factor $h$ out of $h (7 w) + h (8 l)$ .

$h (7 w + 8 l) = s - 7 l w$

Step 4

Divide each term in $h (7 w + 8 l) = s - 7 l w$ by $7 w + 8 l$ and simplify.

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Step 4.1

Divide each term in $h (7 w + 8 l) = s - 7 l w$ by $7 w + 8 l$ .

$\frac{h (7 w + 8 l)}{7 w + 8 l} = \frac{s}{7 w + 8 l} + \frac{- 7 l w}{7 w + 8 l}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $7 w + 8 l$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{h (7 w + 8 l)}{7 w + 8 l} = \frac{s}{7 w + 8 l} + \frac{- 7 l w}{7 w + 8 l}$

Step 4.2.1.2

Divide $h$ by $1$ .

$h = \frac{s}{7 w + 8 l} + \frac{- 7 l w}{7 w + 8 l}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Combine the numerators over the common denominator.

$h = \frac{s - 7 l w}{7 w + 8 l}$