Algebra Examples

$f (x) = (a + 1) x + b - 2$

Step 1

Rewrite the equation as $(a + 1) x + b - 2 = f (x)$ .

$(a + 1) x + b - 2 = f (x)$

Step 2

Simplify each term.

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Step 2.1

Apply the distributive property.

$a x + 1 x + b - 2 = f (x)$

Step 2.2

Multiply $x$ by $1$ .

$a x + x + b - 2 = f (x)$

Step 3

Move all terms not containing $a$ to the right side of the equation.

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Step 3.1

Subtract $x$ from both sides of the equation.

$a x + b - 2 = f (x) - x$

Step 3.2

Subtract $b$ from both sides of the equation.

$a x - 2 = f (x) - x - b$

Step 3.3

Add $2$ to both sides of the equation.

$a x = f (x) - x - b + 2$

Step 4

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

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Step 4.1

Divide each term in $a x = f (x) - x - b + 2$ by $x$ .

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

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $x$ .

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Step 4.2.1.1

Cancel the common factor.

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

Step 4.2.1.2

Divide $a$ by $1$ .

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

Step 4.3

Simplify the right side.

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Step 4.3.1

Simplify each term.

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Step 4.3.1.1

Cancel the common factor of $x$ .

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Step 4.3.1.1.1

Cancel the common factor.

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

Step 4.3.1.1.2

Divide $- 1$ by $1$ .

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

Step 4.3.1.2

Move the negative in front of the fraction.

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