Finite Math Examples

$5 (b - x) = 2 b + a x$

Step 1

Simplify $5 (b - x)$ .

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Step 1.1

Rewrite.

$0 + 0 + 5 (b - x) = 2 b + a x$

Step 1.2

Simplify by adding zeros.

$5 (b - x) = 2 b + a x$

Step 1.3

Apply the distributive property.

$5 b + 5 (- x) = 2 b + a x$

Step 1.4

Multiply $- 1$ by $5$ .

$5 b - 5 x = 2 b + a x$

Step 2

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

$5 b - 5 x - a x = 2 b$

Step 3

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

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Step 3.1

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

$- 5 x - a x = 2 b - 5 b$

Step 3.2

Subtract $5 b$ from $2 b$ .

$- 5 x - a x = - 3 b$

Step 4

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

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Step 4.1

Factor $x$ out of $- 5 x$ .

$x \cdot - 5 - a x = - 3 b$

Step 4.2

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

$x \cdot - 5 + x (- a) = - 3 b$

Step 4.3

Factor $x$ out of $x \cdot - 5 + x (- a)$ .

$x (- 5 - a) = - 3 b$

Step 5

Divide each term in $x (- 5 - a) = - 3 b$ by $- 5 - a$ and simplify.

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Step 5.1

Divide each term in $x (- 5 - a) = - 3 b$ by $- 5 - a$ .

$\frac{x (- 5 - a)}{- 5 - a} = \frac{- 3 b}{- 5 - a}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $- 5 - a$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{x (- 5 - a)}{- 5 - a} = \frac{- 3 b}{- 5 - a}$

Step 5.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 3 b}{- 5 - a}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Move the negative in front of the fraction.

$x = - \frac{3 b}{- 5 - a}$

Step 5.3.2

Rewrite $- 5$ as $- 1 (5)$ .

$x = - \frac{3 b}{- 1 (5) - a}$

Step 5.3.3

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

$x = - \frac{3 b}{- 1 (5) - (a)}$

Step 5.3.4

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

$x = - \frac{3 b}{- 1 (5 + a)}$

Step 5.3.5

Simplify the expression.

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Step 5.3.5.1

Move the negative in front of the fraction.

$x = - - \frac{3 b}{5 + a}$

Step 5.3.5.2

Multiply $- 1$ by $- 1$ .

$x = 1 \frac{3 b}{5 + a}$

Step 5.3.5.3

Multiply $\frac{3 b}{5 + a}$ by $1$ .

$x = \frac{3 b}{5 + a}$