Algebra Examples

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

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.

$y, 1$

Step 1.2

The LCM of one and any expression is the expression.

$y$

Step 2

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

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Step 2.1

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

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

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $y$ .

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Step 2.2.1.1

Cancel the common factor.

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

Step 2.2.1.2

Rewrite the expression.

$10 = x y$

Step 3

Solve the equation.

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Step 3.1

Rewrite the equation as $x y = 10$ .

$x y = 10$

Step 3.2

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

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Step 3.2.1

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

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

Step 3.2.2

Simplify the left side.

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Step 3.2.2.1

Cancel the common factor of $x$ .

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Step 3.2.2.1.1

Cancel the common factor.

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

Step 3.2.2.1.2

Divide $y$ by $1$ .

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

Step 4

The given equation $y = \frac{10}{x}$ can not be written as $y = k x$ , so $y$ doesn't vary directly with $x$ .

$y$ doesn't vary directly with $x$