Precalculus Examples

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

Step 1

Simplify $x (a - b)$ .

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Step 1.1

Rewrite.

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

Step 1.2

Simplify by adding zeros.

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

Step 1.3

Apply the distributive property.

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

Step 1.4

Rewrite using the commutative property of multiplication.

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

Step 2

Simplify $m (x - c)$ .

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Step 2.1

Apply the distributive property.

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

Step 2.2

Rewrite using the commutative property of multiplication.

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

Step 3

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

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

Step 4

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

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Step 4.1

Factor $x$ out of $x a$ .

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

Step 4.2

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

$x (a) + x (- 1 b) - m x = - m c$

Step 4.3

Factor $x$ out of $- m x$ .

$x (a) + x (- 1 b) + x (- m) = - m c$

Step 4.4

Factor $x$ out of $x (a) + x (- 1 b)$ .

$x (a - 1 b) + x (- m) = - m c$

Step 4.5

Factor $x$ out of $x (a - 1 b) + x (- m)$ .

$x (a - 1 b - m) = - m c$

Step 5

Rewrite $- 1 b$ as $- b$ .

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

Step 6

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

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Step 6.1

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

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

Step 6.2

Simplify the left side.

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Step 6.2.1

Cancel the common factor of $a - b - m$ .

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Step 6.2.1.1

Cancel the common factor.

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

Step 6.2.1.2

Divide $x$ by $1$ .

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

Step 6.3

Simplify the right side.

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Step 6.3.1

Move the negative in front of the fraction.

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