Algebra Examples

12 + \frac{20}{x} = 10

$12 + \frac{20}{x} = 10$

Step 1

Move all terms not containing

x

$x$ to the right side of the equation.

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Step 1.1

Subtract

12

$12$ from both sides of the equation.

\frac{20}{x} = 10 - 12

$\frac{20}{x} = 10 - 12$

Step 1.2

Subtract

12

$12$ from

10

$10$ .

\frac{20}{x} = - 2

$\frac{20}{x} = - 2$

\frac{20}{x} = - 2

$\frac{20}{x} = - 2$

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, 1

$x, 1$

Step 2.2

The LCM of one and any expression is the expression.

x

$x$

x

$x$

Step 3

Multiply each term in

\frac{20}{x} = - 2

$\frac{20}{x} = - 2$ by

x

$x$ to eliminate the fractions.

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Step 3.1

Multiply each term in

\frac{20}{x} = - 2

$\frac{20}{x} = - 2$ by

x

$x$ .

\frac{20}{x} x = - 2 x

$\frac{20}{x} x = - 2 x$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of

x

$x$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{20}{x} x = - 2 x$

Step 3.2.1.2

Rewrite the expression.

$20 = - 2 x$

Step 4

Solve the equation.

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Step 4.1

Rewrite the equation as

$- 2 x = 20$ .

$- 2 x = 20$

Step 4.2

Divide each term in

$- 2 x = 20$ by

$- 2$ and simplify.

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Step 4.2.1

Divide each term in

$- 2 x = 20$ by

$- 2$ .

$\frac{- 2 x}{- 2} = \frac{20}{- 2}$

Step 4.2.2

Simplify the left side.

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Step 4.2.2.1

Cancel the common factor of

$- 2$ .

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Step 4.2.2.1.1

Cancel the common factor.

$\frac{- 2 x}{- 2} = \frac{20}{- 2}$

Step 4.2.2.1.2

Divide

$x$ by

$1$ .

$x = \frac{20}{- 2}$

Step 4.2.3

Simplify the right side.

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Step 4.2.3.1

Divide

$20$ by

$- 2$ .

$x = - 10$