Calculus Examples

$x = \frac{0.96 - p}{0.014}$

Step 1

Rewrite the equation as $\frac{0.96 - p}{0.014} = x$ .

$\frac{0.96 - p}{0.014} = x$

Step 2

Multiply both sides by $0.014$ .

$\frac{0.96 - p}{0.014} \cdot 0.014 = x \cdot 0.014$

Step 3

Simplify.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Simplify $\frac{0.96 - p}{0.014} \cdot 0.014$ .

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Step 3.1.1.1

Factor $0.04$ out of $0.96 - p$ .

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Step 3.1.1.1.1

Factor $0.04$ out of $0.96$ .

$\frac{0.04 (24) - p}{0.014} \cdot 0.014 = x \cdot 0.014$

Step 3.1.1.1.2

Factor $0.04$ out of $- p$ .

$\frac{0.04 (24) + 0.04 (- 25 p)}{0.014} \cdot 0.014 = x \cdot 0.014$

Step 3.1.1.1.3

Factor $0.04$ out of $0.04 (24) + 0.04 (- 25 p)$ .

$\frac{0.04 (24 - 25 p)}{0.014} \cdot 0.014 = x \cdot 0.014$

Step 3.1.1.2

Cancel the common factor of $0.04$ .

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Step 3.1.1.2.1

Cancel the common factor.

$\frac{0.04 (24 - 25 p)}{0.014} \cdot 0.014 = x \cdot 0.014$

Step 3.1.1.2.2

Rewrite the expression.

$\frac{24 - 25 p}{0.014} \cdot \frac{0.014}{25} = x \cdot 0.014$

Step 3.1.1.3

Cancel the common factor of $0.014$ .

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Step 3.1.1.3.1

Cancel the common factor.

$\frac{24 - 25 p}{0.014} \cdot \frac{0.014}{25} = x \cdot 0.014$

Step 3.1.1.3.2

Rewrite the expression.

$(24 - 25 p) \cdot \frac{1}{25} = x \cdot 0.014$

Step 3.1.1.4

Apply the distributive property.

$24 (\frac{1}{25}) - 25 p \frac{1}{25} = x \cdot 0.014$

Step 3.1.1.5

Combine $24$ and $\frac{1}{25}$ .

$\frac{24}{25} - 25 p \frac{1}{25} = x \cdot 0.014$

Step 3.1.1.6

Cancel the common factor of $25$ .

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Step 3.1.1.6.1

Factor $25$ out of $- 25 p$ .

$\frac{24}{25} + 25 (- p) \frac{1}{25} = x \cdot 0.014$

Step 3.1.1.6.2

Cancel the common factor.

$\frac{24}{25} + 25 (- p) \frac{1}{25} = x \cdot 0.014$

Step 3.1.1.6.3

Rewrite the expression.

$\frac{24}{25} - p = x \cdot 0.014$

Step 3.1.1.7

Reorder $\frac{24}{25}$ and $- p$ .

$- p + \frac{24}{25} = x \cdot 0.014$

Step 3.2

Simplify the right side.

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Step 3.2.1

Move $0.014$ to the left of $x$ .

$- p + \frac{24}{25} = 0.014 x$

Step 4

Solve for $p$ .

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Step 4.1

Subtract $\frac{24}{25}$ from both sides of the equation.

$- p = 0.014 x - \frac{24}{25}$

Step 4.2

Divide each term in $- p = 0.014 x - \frac{24}{25}$ by $- 1$ and simplify.

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Step 4.2.1

Divide each term in $- p = 0.014 x - \frac{24}{25}$ by $- 1$ .

$\frac{- p}{- 1} = \frac{0.014 x}{- 1} + \frac{- \frac{24}{25}}{- 1}$

Step 4.2.2

Simplify the left side.

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Step 4.2.2.1

Dividing two negative values results in a positive value.

$\frac{p}{1} = \frac{0.014 x}{- 1} + \frac{- \frac{24}{25}}{- 1}$

Step 4.2.2.2

Divide $p$ by $1$ .

$p = \frac{0.014 x}{- 1} + \frac{- \frac{24}{25}}{- 1}$

Step 4.2.3

Simplify the right side.

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Step 4.2.3.1

Simplify each term.

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Step 4.2.3.1.1

Move the negative one from the denominator of $\frac{0.014 x}{- 1}$ .

$p = - 1 \cdot (0.014 x) + \frac{- \frac{24}{25}}{- 1}$

Step 4.2.3.1.2

Rewrite $- 1 \cdot (0.014 x)$ as $- (0.014 x)$ .

$p = - (0.014 x) + \frac{- \frac{24}{25}}{- 1}$

Step 4.2.3.1.3

Multiply $0.014$ by $- 1$ .

$p = - 0.014 x + \frac{- \frac{24}{25}}{- 1}$

Step 4.2.3.1.4

Dividing two negative values results in a positive value.

$p = - 0.014 x + \frac{\frac{24}{25}}{1}$

Step 4.2.3.1.5

Divide $\frac{24}{25}$ by $1$ .

$p = - 0.014 x + \frac{24}{25}$

Step 5

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

$f (x) = - 0.014 x + \frac{24}{25}$