Chemistry Examples

$f (x + 1) = 2 x - 9$

Step 1

Simplify $f (x + 1)$ .

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Step 1.1

Rewrite.

$0 + 0 + f (x + 1) = 2 x - 9$

Step 1.2

Simplify by adding zeros.

$f (x + 1) = 2 x - 9$

Step 1.3

Apply the distributive property.

$f x + f \cdot 1 = 2 x - 9$

Step 1.4

Multiply $f$ by $1$ .

$f x + f = 2 x - 9$

Step 2

Subtract $2 x$ from both sides of the equation.

$f x + f - 2 x = - 9$

Step 3

Subtract $f$ from both sides of the equation.

$f x - 2 x = - 9 - f$

Step 4

Factor $x$ out of $f x - 2 x$ .

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Step 4.1

Factor $x$ out of $f x$ .

$x f - 2 x = - 9 - f$

Step 4.2

Factor $x$ out of $- 2 x$ .

$x f + x \cdot - 2 = - 9 - f$

Step 4.3

Factor $x$ out of $x f + x \cdot - 2$ .

$x (f - 2) = - 9 - f$

Step 5

Divide each term in $x (f - 2) = - 9 - f$ by $f - 2$ and simplify.

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Step 5.1

Divide each term in $x (f - 2) = - 9 - f$ by $f - 2$ .

$\frac{x (f - 2)}{f - 2} = \frac{- 9}{f - 2} + \frac{- f}{f - 2}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $f - 2$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{x (f - 2)}{f - 2} = \frac{- 9}{f - 2} + \frac{- f}{f - 2}$

Step 5.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 9}{f - 2} + \frac{- f}{f - 2}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Combine the numerators over the common denominator.

$x = \frac{- 9 - f}{f - 2}$

Step 5.3.2

Rewrite $- 9$ as $- 1 (9)$ .

$x = \frac{- 1 (9) - f}{f - 2}$

Step 5.3.3

Factor $- 1$ out of $- f$ .

$x = \frac{- 1 (9) - (f)}{f - 2}$

Step 5.3.4

Factor $- 1$ out of $- 1 (9) - (f)$ .

$x = \frac{- 1 (9 + f)}{f - 2}$

Step 5.3.5

Move the negative in front of the fraction.

$x = - \frac{9 + f}{f - 2}$