Algebra Examples

a x + b = c x + d

$a x + b = c x + d$

Step 1

Subtract

c x

$c x$ from both sides of the equation.

a x + b - c x = d

$a x + b - c x = d$

Step 2

Subtract

b

$b$ from both sides of the equation.

a x - c x = d - b

$a x - c x = d - b$

Step 3

Factor

x

$x$ out of

a x - c x

$a x - c x$ .

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Step 3.1

Factor

x

$x$ out of

a x

$a x$ .

x a - c x = d - b

$x a - c x = d - b$

Step 3.2

Factor

x

$x$ out of

- c x

$- c x$ .

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

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

Step 3.3

Factor

x

$x$ out of

x a + x (- c)

$x a + x (- c)$ .

x (a - c) = d - b

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

x (a - c) = d - b

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

Step 4

Divide each term in

x (a - c) = d - b

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

a - c

$a - c$ and simplify.

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Step 4.1

Divide each term in

x (a - c) = d - b

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

a - c

$a - c$ .

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

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

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of

a - c

$a - c$ .

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Step 4.2.1.1

Cancel the common factor.

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

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

Step 4.2.1.2

Divide

x

$x$ by

1

$1$ .

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

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

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

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

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

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

Step 4.3

Simplify the right side.

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Step 4.3.1

Move the negative in front of the fraction.

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

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

Step 4.3.2

Combine the numerators over the common denominator.

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

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

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

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

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

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