Precalculus Examples

$y = \frac{7 - 4 x}{x + 7}$

Step 1

Rewrite the equation as $\frac{7 - 4 x}{x + 7} = y$ .

$\frac{7 - 4 x}{x + 7} = y$

Step 2

Find the LCD of the terms in the equation.

Tap for more steps...

Step 2.1

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

$x + 7, 1$

Step 2.2

Remove parentheses.

$x + 7, 1$

Step 2.3

The LCM of one and any expression is the expression.

$x + 7$

Step 3

Multiply each term in $\frac{7 - 4 x}{x + 7} = y$ by $x + 7$ to eliminate the fractions.

Tap for more steps...

Step 3.1

Multiply each term in $\frac{7 - 4 x}{x + 7} = y$ by $x + 7$ .

$\frac{7 - 4 x}{x + 7} (x + 7) = y (x + 7)$

Step 3.2

Simplify the left side.

Tap for more steps...

Step 3.2.1

Cancel the common factor of $x + 7$ .

Tap for more steps...

Step 3.2.1.1

Cancel the common factor.

$\frac{7 - 4 x}{x + 7} (x + 7) = y (x + 7)$

Step 3.2.1.2

Rewrite the expression.

$7 - 4 x = y (x + 7)$

Step 3.3

Simplify the right side.

Tap for more steps...

Step 3.3.1

Apply the distributive property.

$7 - 4 x = y x + y \cdot 7$

Step 3.3.2

Move $7$ to the left of $y$ .

$7 - 4 x = y x + 7 y$

Step 4

Solve the equation.

Tap for more steps...

Step 4.1

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

$7 - 4 x - y x = 7 y$

Step 4.2

Subtract $7$ from both sides of the equation.

$- 4 x - y x = 7 y - 7$

Step 4.3

Factor $x$ out of $- 4 x - y x$ .

Tap for more steps...

Step 4.3.1

Factor $x$ out of $- 4 x$ .

$x \cdot - 4 - y x = 7 y - 7$

Step 4.3.2

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

$x \cdot - 4 + x (- y) = 7 y - 7$

Step 4.3.3

Factor $x$ out of $x \cdot - 4 + x (- y)$ .

$x (- 4 - y) = 7 y - 7$

Step 4.4

Divide each term in $x (- 4 - y) = 7 y - 7$ by $- 4 - y$ and simplify.

Tap for more steps...

Step 4.4.1

Divide each term in $x (- 4 - y) = 7 y - 7$ by $- 4 - y$ .

$\frac{x (- 4 - y)}{- 4 - y} = \frac{7 y}{- 4 - y} + \frac{- 7}{- 4 - y}$

Step 4.4.2

Simplify the left side.

Tap for more steps...

Step 4.4.2.1

Cancel the common factor of $- 4 - y$ .

Tap for more steps...

Step 4.4.2.1.1

Cancel the common factor.

$\frac{x (- 4 - y)}{- 4 - y} = \frac{7 y}{- 4 - y} + \frac{- 7}{- 4 - y}$

Step 4.4.2.1.2

Divide $x$ by $1$ .

$x = \frac{7 y}{- 4 - y} + \frac{- 7}{- 4 - y}$

Step 4.4.3

Simplify the right side.

Tap for more steps...

Step 4.4.3.1

Combine the numerators over the common denominator.

$x = \frac{7 y - 7}{- 4 - y}$

Step 4.4.3.2

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

Tap for more steps...

Step 4.4.3.2.1

Factor $7$ out of $7 y$ .

$x = \frac{7 (y) - 7}{- 4 - y}$

Step 4.4.3.2.2

Factor $7$ out of $- 7$ .

$x = \frac{7 (y) + 7 (- 1)}{- 4 - y}$

Step 4.4.3.2.3

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

$x = \frac{7 (y - 1)}{- 4 - y}$

Step 4.4.3.3

Rewrite $- 4$ as $- 1 (4)$ .

$x = \frac{7 (y - 1)}{- 1 (4) - y}$

Step 4.4.3.4

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

$x = \frac{7 (y - 1)}{- 1 (4) - (y)}$

Step 4.4.3.5

Factor $- 1$ out of $- 1 (4) - (y)$ .

$x = \frac{7 (y - 1)}{- 1 (4 + y)}$

Step 4.4.3.6

Move the negative in front of the fraction.

$x = - \frac{7 (y - 1)}{4 + y}$