Finite Math Examples

$y = \frac{1}{7 x} + 2$

Step 1

Rewrite the equation as $\frac{1}{7 x} + 2 = y$ .

$\frac{1}{7 x} + 2 = y$

Step 2

Subtract $2$ from both sides of the equation.

$\frac{1}{7 x} = y - 2$

Step 3

Find the LCD of the terms in the equation.

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Step 3.1

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

$7 x, 1, 1$

Step 3.2

The LCM of one and any expression is the expression.

$7 x$

Step 4

Multiply each term in $\frac{1}{7 x} = y - 2$ by $7 x$ to eliminate the fractions.

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Step 4.1

Multiply each term in $\frac{1}{7 x} = y - 2$ by $7 x$ .

$\frac{1}{7 x} (7 x) = y (7 x) - 2 (7 x)$

Step 4.2

Simplify the left side.

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Step 4.2.1

Rewrite using the commutative property of multiplication.

$7 \frac{1}{7 x} x = y (7 x) - 2 (7 x)$

Step 4.2.2

Cancel the common factor of $7$ .

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Step 4.2.2.1

Factor $7$ out of $7 x$ .

$7 \frac{1}{7 (x)} x = y (7 x) - 2 (7 x)$

Step 4.2.2.2

Cancel the common factor.

$7 \frac{1}{7 x} x = y (7 x) - 2 (7 x)$

Step 4.2.2.3

Rewrite the expression.

$\frac{1}{x} x = y (7 x) - 2 (7 x)$

Step 4.2.3

Cancel the common factor of $x$ .

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Step 4.2.3.1

Cancel the common factor.

$\frac{1}{x} x = y (7 x) - 2 (7 x)$

Step 4.2.3.2

Rewrite the expression.

$1 = y (7 x) - 2 (7 x)$

Step 4.3

Simplify the right side.

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Step 4.3.1

Simplify each term.

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Step 4.3.1.1

Rewrite using the commutative property of multiplication.

$1 = 7 y x - 2 (7 x)$

Step 4.3.1.2

Multiply $7$ by $- 2$ .

$1 = 7 y x - 14 x$

Step 5

Solve the equation.

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Step 5.1

Rewrite the equation as $7 y x - 14 x = 1$ .

$7 y x - 14 x = 1$

Step 5.2

Factor $7 x$ out of $7 y x - 14 x$ .

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Step 5.2.1

Factor $7 x$ out of $7 y x$ .

$7 x (y) - 14 x = 1$

Step 5.2.2

Factor $7 x$ out of $- 14 x$ .

$7 x (y) + 7 x (- 2) = 1$

Step 5.2.3

Factor $7 x$ out of $7 x (y) + 7 x (- 2)$ .

$7 x (y - 2) = 1$

Step 5.3

Divide each term in $7 x (y - 2) = 1$ by $7 (y - 2)$ and simplify.

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Step 5.3.1

Divide each term in $7 x (y - 2) = 1$ by $7 (y - 2)$ .

$\frac{7 x (y - 2)}{7 (y - 2)} = \frac{1}{7 (y - 2)}$

Step 5.3.2

Simplify the left side.

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Step 5.3.2.1

Cancel the common factor of $7$ .

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Step 5.3.2.1.1

Cancel the common factor.

$\frac{7 x (y - 2)}{7 (y - 2)} = \frac{1}{7 (y - 2)}$

Step 5.3.2.1.2

Rewrite the expression.

$\frac{x (y - 2)}{y - 2} = \frac{1}{7 (y - 2)}$

Step 5.3.2.2

Cancel the common factor of $y - 2$ .

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Step 5.3.2.2.1

Cancel the common factor.

$\frac{x (y - 2)}{y - 2} = \frac{1}{7 (y - 2)}$

Step 5.3.2.2.2

Divide $x$ by $1$ .

$x = \frac{1}{7 (y - 2)}$