Pre-Algebra Examples

$w = \frac{8 y - x}{y}$

Step 1

Rewrite the equation as $\frac{8 y - x}{y} = w$ .

$\frac{8 y - x}{y} = w$

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.

$y, 1$

Step 2.2

The LCM of one and any expression is the expression.

$y$

Step 3

Multiply each term in $\frac{8 y - x}{y} = w$ by $y$ to eliminate the fractions.

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Step 3.1

Multiply each term in $\frac{8 y - x}{y} = w$ by $y$ .

$\frac{8 y - x}{y} y = w y$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $y$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{8 y - x}{y} y = w y$

Step 3.2.1.2

Rewrite the expression.

$8 y - x = w y$

Step 4

Solve the equation.

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Step 4.1

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

$8 y - x - w y = 0$

Step 4.2

Add $x$ to both sides of the equation.

$8 y - w y = x$

Step 4.3

Factor $y$ out of $8 y - w y$ .

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Step 4.3.1

Factor $y$ out of $8 y$ .

$y \cdot 8 - w y = x$

Step 4.3.2

Factor $y$ out of $- w y$ .

$y \cdot 8 + y (- w) = x$

Step 4.3.3

Factor $y$ out of $y \cdot 8 + y (- w)$ .

$y (8 - w) = x$

Step 4.4

Divide each term in $y (8 - w) = x$ by $8 - w$ and simplify.

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Step 4.4.1

Divide each term in $y (8 - w) = x$ by $8 - w$ .

$\frac{y (8 - w)}{8 - w} = \frac{x}{8 - w}$

Step 4.4.2

Simplify the left side.

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Step 4.4.2.1

Cancel the common factor of $8 - w$ .

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Step 4.4.2.1.1

Cancel the common factor.

$\frac{y (8 - w)}{8 - w} = \frac{x}{8 - w}$

Step 4.4.2.1.2

Divide $y$ by $1$ .

$y = \frac{x}{8 - w}$