Precalculus Examples

$a (x + b) = b x + c$

Step 1

Simplify $a (x + b)$ .

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Step 1.1

Rewrite.

$0 + 0 + a (x + b) = b x + c$

Step 1.2

Simplify by adding zeros.

$a (x + b) = b x + c$

Step 1.3

Apply the distributive property.

$a x + a b = b x + c$

Step 2

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

$a x + a b - b x = c$

Step 3

Subtract $a b$ from both sides of the equation.

$a x - b x = c - a b$

Step 4

Factor $x$ out of $a x - b x$ .

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Step 4.1

Factor $x$ out of $a x$ .

$x a - b x = c - a b$

Step 4.2

Factor $x$ out of $- b x$ .

$x a + x (- b) = c - a b$

Step 4.3

Factor $x$ out of $x a + x (- b)$ .

$x (a - b) = c - a b$

Step 5

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

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Step 5.1

Divide each term in $x (a - b) = c - a b$ by $a - b$ .

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

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $a - b$ .

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Step 5.2.1.1

Cancel the common factor.

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

Step 5.2.1.2

Divide $x$ by $1$ .

$x = \frac{c}{a - b} + \frac{- a b}{a - b}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Combine the numerators over the common denominator.

$x = \frac{c - a b}{a - b}$