Precalculus Examples

$y = \frac{5 - x}{7 x + 11}$

Step 1

Rewrite the equation as $\frac{5 - x}{7 x + 11} = y$ .

$\frac{5 - x}{7 x + 11} = y$

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.

$7 x + 11, 1$

Step 2.2

Remove parentheses.

$7 x + 11, 1$

Step 2.3

The LCM of one and any expression is the expression.

$7 x + 11$

Step 3

Multiply each term in $\frac{5 - x}{7 x + 11} = y$ by $7 x + 11$ to eliminate the fractions.

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Step 3.1

Multiply each term in $\frac{5 - x}{7 x + 11} = y$ by $7 x + 11$ .

$\frac{5 - x}{7 x + 11} (7 x + 11) = y (7 x + 11)$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $7 x + 11$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{5 - x}{7 x + 11} (7 x + 11) = y (7 x + 11)$

Step 3.2.1.2

Rewrite the expression.

$5 - x = y (7 x + 11)$

Step 3.3

Simplify the right side.

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Step 3.3.1

Apply the distributive property.

$5 - x = y (7 x) + y \cdot 11$

Step 3.3.2

Reorder.

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Step 3.3.2.1

Rewrite using the commutative property of multiplication.

$5 - x = 7 y x + y \cdot 11$

Step 3.3.2.2

Move $11$ to the left of $y$ .

$5 - x = 7 y x + 11 y$

Step 4

Solve the equation.

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Step 4.1

Subtract $7 y x$ from both sides of the equation.

$5 - x - 7 y x = 11 y$

Step 4.2

Subtract $5$ from both sides of the equation.

$- x - 7 y x = 11 y - 5$

Step 4.3

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

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Step 4.3.1

Factor $x$ out of $- x$ .

$x \cdot - 1 - 7 y x = 11 y - 5$

Step 4.3.2

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

$x \cdot - 1 + x (- 7 y) = 11 y - 5$

Step 4.3.3

Factor $x$ out of $x \cdot - 1 + x (- 7 y)$ .

$x (- 1 - 7 y) = 11 y - 5$

Step 4.4

Divide each term in $x (- 1 - 7 y) = 11 y - 5$ by $- 1 - 7 y$ and simplify.

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Step 4.4.1

Divide each term in $x (- 1 - 7 y) = 11 y - 5$ by $- 1 - 7 y$ .

$\frac{x (- 1 - 7 y)}{- 1 - 7 y} = \frac{11 y}{- 1 - 7 y} + \frac{- 5}{- 1 - 7 y}$

Step 4.4.2

Simplify the left side.

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Step 4.4.2.1

Cancel the common factor of $- 1 - 7 y$ .

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Step 4.4.2.1.1

Cancel the common factor.

$\frac{x (- 1 - 7 y)}{- 1 - 7 y} = \frac{11 y}{- 1 - 7 y} + \frac{- 5}{- 1 - 7 y}$

Step 4.4.2.1.2

Divide $x$ by $1$ .

$x = \frac{11 y}{- 1 - 7 y} + \frac{- 5}{- 1 - 7 y}$

Step 4.4.3

Simplify the right side.

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Step 4.4.3.1

Combine the numerators over the common denominator.

$x = \frac{11 y - 5}{- 1 - 7 y}$

Step 4.4.3.2

Rewrite $- 1$ as $- 1 (1)$ .

$x = \frac{11 y - 5}{- 1 (1) - 7 y}$

Step 4.4.3.3

Factor $- 1$ out of $- 7 y$ .

$x = \frac{11 y - 5}{- 1 (1) - (7 y)}$

Step 4.4.3.4

Factor $- 1$ out of $- 1 (1) - (7 y)$ .

$x = \frac{11 y - 5}{- 1 (1 + 7 y)}$

Step 4.4.3.5

Move the negative in front of the fraction.

$x = - \frac{11 y - 5}{1 + 7 y}$