Precalculus Examples

$a (n) = 8 n - 1$

Step 1

Subtract $8 n$ from both sides of the equation.

$a n - 8 n = - 1$

Step 2

Factor $n$ out of $a n - 8 n$ .

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Step 2.1

Factor $n$ out of $a n$ .

$n a - 8 n = - 1$

Step 2.2

Factor $n$ out of $- 8 n$ .

$n a + n \cdot - 8 = - 1$

Step 2.3

Factor $n$ out of $n a + n \cdot - 8$ .

$n (a - 8) = - 1$

Step 3

Divide each term in $n (a - 8) = - 1$ by $a - 8$ and simplify.

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Step 3.1

Divide each term in $n (a - 8) = - 1$ by $a - 8$ .

$\frac{n (a - 8)}{a - 8} = \frac{- 1}{a - 8}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $a - 8$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{n (a - 8)}{a - 8} = \frac{- 1}{a - 8}$

Step 3.2.1.2

Divide $n$ by $1$ .

$n = \frac{- 1}{a - 8}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Move the negative in front of the fraction.

$n = - \frac{1}{a - 8}$

Step 4

To rewrite as a function of $a$ , write the equation so that $n$ is by itself on one side of the equal sign and an expression involving only $a$ is on the other side.

$f (a) = - \frac{1}{a - 8}$