Algebra Examples

$\frac{x}{x + 5} = 10$

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.

$x + 5, 1$

Step 1.2

Remove parentheses.

$x + 5, 1$

Step 1.3

The LCM of one and any expression is the expression.

$x + 5$

Step 2

Multiply each term in $\frac{x}{x + 5} = 10$ by $x + 5$ to eliminate the fractions.

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Step 2.1

Multiply each term in $\frac{x}{x + 5} = 10$ by $x + 5$ .

$\frac{x}{x + 5} (x + 5) = 10 (x + 5)$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $x + 5$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{x}{x + 5} (x + 5) = 10 (x + 5)$

Step 2.2.1.2

Rewrite the expression.

$x = 10 (x + 5)$

Step 2.3

Simplify the right side.

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Step 2.3.1

Apply the distributive property.

$x = 10 x + 10 \cdot 5$

Step 2.3.2

Multiply $10$ by $5$ .

$x = 10 x + 50$

Step 3

Solve the equation.

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Step 3.1

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

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Step 3.1.1

Subtract $10 x$ from both sides of the equation.

$x - 10 x = 50$

Step 3.1.2

Subtract $10 x$ from $x$ .

$- 9 x = 50$

Step 3.2

Divide each term in $- 9 x = 50$ by $- 9$ and simplify.

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Step 3.2.1

Divide each term in $- 9 x = 50$ by $- 9$ .

$\frac{- 9 x}{- 9} = \frac{50}{- 9}$

Step 3.2.2

Simplify the left side.

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Step 3.2.2.1

Cancel the common factor of $- 9$ .

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Step 3.2.2.1.1

Cancel the common factor.

$\frac{- 9 x}{- 9} = \frac{50}{- 9}$

Step 3.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{50}{- 9}$

Step 3.2.3

Simplify the right side.

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Step 3.2.3.1

Move the negative in front of the fraction.

$x = - \frac{50}{9}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{50}{9}$

Decimal Form:

$x = - 5.\overline{5}$

Mixed Number Form:

$x = - 5 \frac{5}{9}$