Algebra Examples

$\frac{1}{x - 3} = 10$

Step 1

Find the LCD of the terms in the equation.

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Step 1.1

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

$x - 3, 1$

Step 1.2

Remove parentheses.

$x - 3, 1$

Step 1.3

The LCM of one and any expression is the expression.

$x - 3$

Step 2

Multiply each term in $\frac{1}{x - 3} = 10$ by $x - 3$ to eliminate the fractions.

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Step 2.1

Multiply each term in $\frac{1}{x - 3} = 10$ by $x - 3$ .

$\frac{1}{x - 3} (x - 3) = 10 (x - 3)$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $x - 3$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{1}{x - 3} (x - 3) = 10 (x - 3)$

Step 2.2.1.2

Rewrite the expression.

$1 = 10 (x - 3)$

Step 2.3

Simplify the right side.

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Step 2.3.1

Apply the distributive property.

$1 = 10 x + 10 \cdot - 3$

Step 2.3.2

Multiply $10$ by $- 3$ .

$1 = 10 x - 30$

Step 3

Solve the equation.

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Step 3.1

Rewrite the equation as $10 x - 30 = 1$ .

$10 x - 30 = 1$

Step 3.2

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

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Step 3.2.1

Add $30$ to both sides of the equation.

$10 x = 1 + 30$

Step 3.2.2

Add $1$ and $30$ .

$10 x = 31$

Step 3.3

Divide each term in $10 x = 31$ by $10$ and simplify.

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Step 3.3.1

Divide each term in $10 x = 31$ by $10$ .

$\frac{10 x}{10} = \frac{31}{10}$

Step 3.3.2

Simplify the left side.

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Step 3.3.2.1

Cancel the common factor of $10$ .

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Step 3.3.2.1.1

Cancel the common factor.

$\frac{10 x}{10} = \frac{31}{10}$

Step 3.3.2.1.2

Divide $x$ by $1$ .

$x = \frac{31}{10}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{31}{10}$

Decimal Form:

$x = 3.1$

Mixed Number Form:

$x = 3 \frac{1}{10}$