Precalculus Examples

$l e n g t h = 4$ , $e = \frac{1}{5}$

Step 1

Solve the equation for $l$ .

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Simplify.

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Combine $l$ and $\frac{1}{5}$ .

$\frac{l}{5} \cdot (n g t h) = 4$

$e = \frac{1}{5}$

Combine $n$ and $\frac{l}{5}$ .

$\frac{n l}{5} \cdot (g t h) = 4$

$e = \frac{1}{5}$

Combine $g$ and $\frac{n l}{5}$ .

$\frac{g (n l)}{5} \cdot (t h) = 4$

$e = \frac{1}{5}$

Combine $t$ and $\frac{g (n l)}{5}$ .

$\frac{t (g (n l))}{5} \cdot h = 4$

$e = \frac{1}{5}$

Combine $\frac{t (g (n l))}{5}$ and $h$ .

$\frac{t (g (n l)) h}{5} = 4$

$e = \frac{1}{5}$

Remove parentheses.

$\frac{t (g n l) h}{5} = 4$

$e = \frac{1}{5}$

Remove parentheses.

$\frac{t (g n) l h}{5} = 4$

$e = \frac{1}{5}$

Remove parentheses.

$\frac{t g n l h}{5} = 4$

$e = \frac{1}{5}$

$\frac{t g n l h}{5} = 4$

$e = \frac{1}{5}$

Divide each term in $\frac{t g n l h}{5} = 4$ by $\frac{1}{5} n g t h$ and simplify.

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Divide each term in $\frac{t g n l h}{5} = 4$ by $\frac{1}{5} n g t h$ .

$\frac{\frac{t g n l h}{5}}{\frac{1}{5} \cdot (n g t h)} = \frac{4}{\frac{1}{5} \cdot (n g t h)}$

$e = \frac{1}{5}$

Simplify the left side.

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Multiply the numerator by the reciprocal of the denominator.

$\frac{t g n l h}{5} \cdot \frac{1}{\frac{1}{5} \cdot (n g t h)} = \frac{4}{\frac{1}{5} \cdot (n g t h)}$

$e = \frac{1}{5}$

Cancel the common factor of $n g t h$ .

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Factor $n g t h$ out of $t g n l h$ .

$\frac{n g t h (l)}{5} \cdot \frac{1}{\frac{1}{5} \cdot (n g t h)} = \frac{4}{\frac{1}{5} \cdot (n g t h)}$

$e = \frac{1}{5}$

Factor $n g t h$ out of $\frac{1}{5} n g t h$ .

$\frac{n g t h (l)}{5} \cdot \frac{1}{n g t h (\frac{1}{5})} = \frac{4}{\frac{1}{5} \cdot (n g t h)}$

$e = \frac{1}{5}$

Cancel the common factor.

$\frac{n g t h l}{5} \cdot \frac{1}{n g t h (\frac{1}{5})} = \frac{4}{\frac{1}{5} \cdot (n g t h)}$

$e = \frac{1}{5}$

Rewrite the expression.

$\frac{l}{5} \cdot \frac{1}{\frac{1}{5}} = \frac{4}{\frac{1}{5} \cdot (n g t h)}$

$e = \frac{1}{5}$

$\frac{l}{5} \cdot \frac{1}{\frac{1}{5}} = \frac{4}{\frac{1}{5} \cdot (n g t h)}$

$e = \frac{1}{5}$

Multiply $\frac{l}{5}$ by $\frac{1}{\frac{1}{5}}$ .

$\frac{l}{5 (\frac{1}{5})} = \frac{4}{\frac{1}{5} \cdot (n g t h)}$

$e = \frac{1}{5}$

Combine $5$ and $\frac{1}{5}$ .

$\frac{l}{\frac{5}{5}} = \frac{4}{\frac{1}{5} \cdot (n g t h)}$

$e = \frac{1}{5}$

Cancel the common factor of $5$ .

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Cancel the common factor.

$\frac{l}{\frac{5}{5}} = \frac{4}{\frac{1}{5} \cdot (n g t h)}$

$e = \frac{1}{5}$

Rewrite the expression.

$\frac{l}{1} = \frac{4}{\frac{1}{5} \cdot (n g t h)}$

$e = \frac{1}{5}$

$\frac{l}{1} = \frac{4}{\frac{1}{5} \cdot (n g t h)}$

$e = \frac{1}{5}$

Divide $l$ by $1$ .

$l = \frac{4}{\frac{1}{5} \cdot (n g t h)}$

$e = \frac{1}{5}$

$l = \frac{4}{\frac{1}{5} \cdot (n g t h)}$

$e = \frac{1}{5}$

Simplify the right side.

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Simplify the denominator.

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Combine $\frac{1}{5}$ and $n$ .

$l = \frac{4}{\frac{n}{5} \cdot (g t h)}$

$e = \frac{1}{5}$

Combine $\frac{n}{5}$ and $g$ .

$l = \frac{4}{\frac{n g}{5} \cdot (t h)}$

$e = \frac{1}{5}$

Combine $\frac{n g}{5}$ and $t$ .

$l = \frac{4}{\frac{n g t}{5} \cdot h}$

$e = \frac{1}{5}$

Combine $\frac{n g t}{5}$ and $h$ .

$l = \frac{4}{\frac{n g t h}{5}}$

$e = \frac{1}{5}$

$l = \frac{4}{\frac{n g t h}{5}}$

$e = \frac{1}{5}$

Multiply the numerator by the reciprocal of the denominator.

$l = 4 (\frac{5}{n g t h})$

$e = \frac{1}{5}$

Multiply $4 \frac{5}{n g t h}$ .

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Combine $4$ and $\frac{5}{n g t h}$ .

$l = \frac{4 \cdot 5}{n g t h}$

$e = \frac{1}{5}$

Multiply $4$ by $5$ .

$l = \frac{20}{n g t h}$

$e = \frac{1}{5}$

$l = \frac{20}{n g t h}$

$e = \frac{1}{5}$

$l = \frac{20}{n g t h}$

$e = \frac{1}{5}$

$l = \frac{20}{n g t h}$

$e = \frac{1}{5}$

$l = \frac{20}{n g t h}$

$e = \frac{1}{5}$

Step 2

Solve the equation for $n$ .

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Simplify $(\frac{20}{n g t h}) \cdot (\frac{1}{5}) \cdot (n g t h)$ .

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Cancel the common factor of $5$ .

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Factor $5$ out of $20$ .

$\frac{5 (4)}{n g t h} \cdot \frac{1}{5} \cdot (n g t h) = 4$

$e = \frac{1}{5}$

Cancel the common factor.

$\frac{5 \cdot 4}{n g t h} \cdot \frac{1}{5} \cdot (n g t h) = 4$

$e = \frac{1}{5}$

Rewrite the expression.

$\frac{4}{n g t h} \cdot (n g t h) = 4$

$e = \frac{1}{5}$

$\frac{4}{n g t h} \cdot (n g t h) = 4$

$e = \frac{1}{5}$

Cancel the common factor of $n g t h$ .

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Cancel the common factor.

$\frac{4}{n g t h} \cdot (n g t h) = 4$

$e = \frac{1}{5}$

Rewrite the expression.

$4 = 4$

$e = \frac{1}{5}$

$4 = 4$

$e = \frac{1}{5}$

$4 = 4$

$e = \frac{1}{5}$

Since $4 = 4$ , the equation will always be true.

Always true

$e = \frac{1}{5}$

Always true

$e = \frac{1}{5}$

Step 3

Reduce the system.

Always $t r u (\frac{1}{5})$

$e = \frac{1}{5}$