Algebra Examples

$(\frac{1}{x}) (\frac{x - 1}{2}) = 4$

Step 1

Factor each term.

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Step 1.1

Multiply $\frac{1}{x}$ by $\frac{x - 1}{2}$ .

$\frac{1}{x} (\frac{x - 1}{2}) = 4$

Step 1.2

Multiply $\frac{1}{x}$ by $\frac{x - 1}{2}$ .

$\frac{x - 1}{x \cdot 2} = 4$

Step 2

Find the LCD of the terms in the equation.

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Step 2.1

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$x \cdot 2, 1$

Step 2.2

Remove parentheses.

$x \cdot 2, 1$

Step 2.3

The LCM of one and any expression is the expression.

$x \cdot 2$

Step 3

Multiply each term in $\frac{x - 1}{x \cdot 2} = 4$ by $x \cdot 2$ to eliminate the fractions.

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Step 3.1

Multiply each term in $\frac{x - 1}{x \cdot 2} = 4$ by $x \cdot 2$ .

$\frac{x - 1}{x \cdot 2} (x \cdot 2) = 4 (x \cdot 2)$

Step 3.2

Simplify the left side.

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Step 3.2.1

Rewrite using the commutative property of multiplication.

$2 \frac{x - 1}{x \cdot 2} x = 4 (x \cdot 2)$

Step 3.2.2

Cancel the common factor of $2$ .

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Step 3.2.2.1

Factor $2$ out of $x \cdot 2$ .

$2 \frac{x - 1}{2 \cdot x} x = 4 (x \cdot 2)$

Step 3.2.2.2

Cancel the common factor.

$2 \frac{x - 1}{2 \cdot x} x = 4 (x \cdot 2)$

Step 3.2.2.3

Rewrite the expression.

$\frac{x - 1}{x} x = 4 (x \cdot 2)$

Step 3.2.3

Cancel the common factor of $x$ .

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Step 3.2.3.1

Cancel the common factor.

$\frac{x - 1}{x} x = 4 (x \cdot 2)$

Step 3.2.3.2

Rewrite the expression.

$x - 1 = 4 (x \cdot 2)$

Step 3.3

Simplify the right side.

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Step 3.3.1

Move $2$ to the left of $x$ .

$x - 1 = 4 (2 \cdot x)$

Step 3.3.2

Multiply $2$ by $4$ .

$x - 1 = 8 x$

Step 4

Solve the equation.

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Step 4.1

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

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Step 4.1.1

Subtract $8 x$ from both sides of the equation.

$x - 1 - 8 x = 0$

Step 4.1.2

Subtract $8 x$ from $x$ .

$- 7 x - 1 = 0$

Step 4.2

Add $1$ to both sides of the equation.

$- 7 x = 1$

Step 4.3

Divide each term in $- 7 x = 1$ by $- 7$ and simplify.

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Step 4.3.1

Divide each term in $- 7 x = 1$ by $- 7$ .

$\frac{- 7 x}{- 7} = \frac{1}{- 7}$

Step 4.3.2

Simplify the left side.

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Step 4.3.2.1

Cancel the common factor of $- 7$ .

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Step 4.3.2.1.1

Cancel the common factor.

$\frac{- 7 x}{- 7} = \frac{1}{- 7}$

Step 4.3.2.1.2

Divide $x$ by $1$ .

$x = \frac{1}{- 7}$

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.

$x = - \frac{1}{7}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{1}{7}$

Decimal Form:

$x = - 0.\overline{142857}$