Algebra Examples

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

Step 1

Multiply $\frac{a}{b}$ by $x - 1$ .

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

Step 2

Move all terms containing $x$ to the left side of the equation.

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Step 2.1

Subtract $\frac{a (x - 1)}{b}$ from both sides of the equation.

$3 x - \frac{a (x - 1)}{b} = 0$

Step 2.2

To write $3 x$ as a fraction with a common denominator, multiply by $\frac{b}{b}$ .

$\frac{3 x b}{b} - \frac{a (x - 1)}{b} = 0$

Step 2.3

Combine the numerators over the common denominator.

$\frac{3 x b - a (x - 1)}{b} = 0$

Step 2.4

Simplify the numerator.

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Step 2.4.1

Apply the distributive property.

$\frac{3 x b - a x - a \cdot - 1}{b} = 0$

Step 2.4.2

Multiply $- a \cdot - 1$ .

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Step 2.4.2.1

Multiply $- 1$ by $- 1$ .

$\frac{3 x b - a x + 1 a}{b} = 0$

Step 2.4.2.2

Multiply $a$ by $1$ .

$\frac{3 x b - a x + a}{b} = 0$

Step 3

Set the numerator equal to zero.

$3 x b - a x + a = 0$

Step 4

Solve the equation for $x$ .

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Step 4.1

Subtract $a$ from both sides of the equation.

$3 x b - a x = - a$

Step 4.2

Factor $x$ out of $3 x b - a x$ .

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Step 4.2.1

Factor $x$ out of $3 x b$ .

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

Step 4.2.2

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

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

Step 4.2.3

Factor $x$ out of $x (3 b) + x (- a)$ .

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

Step 4.3

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

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Step 4.3.1

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

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

Step 4.3.2

Simplify the left side.

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Step 4.3.2.1

Cancel the common factor of $3 b - a$ .

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Step 4.3.2.1.1

Cancel the common factor.

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

Step 4.3.2.1.2

Divide $x$ by $1$ .

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

Step 4.3.3

Simplify the right side.

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Step 4.3.3.1

Move the negative in front of the fraction.

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