Algebra Examples

$a \cdot (5 - x) = b x - 8$

Step 1

Simplify $a \cdot (5 - x)$ .

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Step 1.1

Rewrite.

$0 + 0 + a \cdot (5 - x) = b x - 8$

Step 1.2

Simplify by adding zeros.

$a \cdot (5 - x) = b x - 8$

Step 1.3

Apply the distributive property.

$a \cdot 5 + a (- x) = b x - 8$

Step 1.4

Reorder.

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Step 1.4.1

Move $5$ to the left of $a$ .

$5 \cdot a + a (- x) = b x - 8$

Step 1.4.2

Rewrite using the commutative property of multiplication.

$5 a - a x = b x - 8$

Step 2

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

$5 a - a x - b x = - 8$

Step 3

Subtract $5 a$ from both sides of the equation.

$- a x - b x = - 8 - 5 a$

Step 4

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

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Step 4.1

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

$x (- a) - b x = - 8 - 5 a$

Step 4.2

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

$x (- a) + x (- b) = - 8 - 5 a$

Step 4.3

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

$x (- a - b) = - 8 - 5 a$

Step 5

Divide each term in $x (- a - b) = - 8 - 5 a$ by $- a - b$ and simplify.

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Step 5.1

Divide each term in $x (- a - b) = - 8 - 5 a$ by $- a - b$ .

$\frac{x (- a - b)}{- a - b} = \frac{- 8}{- a - b} + \frac{- 5 a}{- a - b}$

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.

$\frac{x (- a - b)}{- a - b} = \frac{- 8}{- a - b} + \frac{- 5 a}{- a - b}$

Step 5.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 8}{- a - b} + \frac{- 5 a}{- a - b}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Combine the numerators over the common denominator.

$x = \frac{- 8 - 5 a}{- a - b}$

Step 5.3.2

Rewrite $- 8$ as $- 1 (8)$ .

$x = \frac{- 1 (8) - 5 a}{- a - b}$

Step 5.3.3

Factor $- 1$ out of $- 5 a$ .

$x = \frac{- 1 (8) - (5 a)}{- a - b}$

Step 5.3.4

Factor $- 1$ out of $- 1 (8) - (5 a)$ .

$x = \frac{- 1 (8 + 5 a)}{- a - b}$

Step 5.3.5

Factor $- 1$ out of $- a$ .

$x = \frac{- 1 (8 + 5 a)}{- (a) - b}$

Step 5.3.6

Factor $- 1$ out of $- b$ .

$x = \frac{- 1 (8 + 5 a)}{- (a) - (b)}$

Step 5.3.7

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

$x = \frac{- 1 (8 + 5 a)}{- (a + b)}$

Step 5.3.8

Rewrite $- (a + b)$ as $- 1 (a + b)$ .

$x = \frac{- 1 (8 + 5 a)}{- 1 (a + b)}$

Step 5.3.9

Cancel the common factor.

$x = \frac{- 1 (8 + 5 a)}{- 1 (a + b)}$

Step 5.3.10

Rewrite the expression.

$x = \frac{8 + 5 a}{a + b}$