Calculus Examples

$\frac{c (x)}{x} = 165 + 8.9 x$

Step 1

Reduce the expression by cancelling the common factors.

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Step 1.1

Reduce the expression $\frac{c x}{x}$ by cancelling the common factors.

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Step 1.1.1

Cancel the common factor.

$\frac{c x}{x} = 165 + 8.9 x$

Step 1.1.2

Rewrite the expression.

$\frac{c}{1} = 165 + 8.9 x$

Step 1.2

Divide $c$ by $1$ .

$c = 165 + 8.9 x$

Step 2

Solve the equation.

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Step 2.1

Rewrite the equation as $165 + 8.9 x = c$ .

$165 + 8.9 x = c$

Step 2.2

Subtract $165$ from both sides of the equation.

$8.9 x = c - 165$

Step 2.3

Divide each term in $8.9 x = c - 165$ by $8.9$ and simplify.

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Step 2.3.1

Divide each term in $8.9 x = c - 165$ by $8.9$ .

$\frac{8.9 x}{8.9} = \frac{c}{8.9} + \frac{- 165}{8.9}$

Step 2.3.2

Simplify the left side.

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Step 2.3.2.1

Cancel the common factor of $8.9$ .

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Step 2.3.2.1.1

Cancel the common factor.

$\frac{8.9 x}{8.9} = \frac{c}{8.9} + \frac{- 165}{8.9}$

Step 2.3.2.1.2

Divide $x$ by $1$ .

$x = \frac{c}{8.9} + \frac{- 165}{8.9}$

Step 2.3.3

Simplify the right side.

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Step 2.3.3.1

Simplify each term.

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Step 2.3.3.1.1

Multiply by $1$ .

$x = \frac{1 c}{8.9} + \frac{- 165}{8.9}$

Step 2.3.3.1.2

Factor $8.9$ out of $8.9$ .

$x = \frac{1 c}{8.9 (1)} + \frac{- 165}{8.9}$

Step 2.3.3.1.3

Separate fractions.

$x = \frac{1}{8.9} \cdot \frac{c}{1} + \frac{- 165}{8.9}$

Step 2.3.3.1.4

Divide $1$ by $8.9$ .

$x = 0.11235955 \frac{c}{1} + \frac{- 165}{8.9}$

Step 2.3.3.1.5

Divide $c$ by $1$ .

$x = 0.11235955 c + \frac{- 165}{8.9}$

Step 2.3.3.1.6

Divide $- 165$ by $8.9$ .

$x = 0.11235955 c - 18.53932584$

Step 3

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

$f (c) = 0.11235955 c - 18.53932584$