Precalculus Examples

$x = | 2 y |$

Step 1

Rewrite the equation as $| 2 y | = x$ .

$| 2 y | = x$

Step 2

Remove the absolute value term. This creates a $\pm$ on the right side of the equation because $| x | = \pm x$ .

$2 y = \pm x$

Step 3

The complete solution is the result of both the positive and negative portions of the solution.

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Step 3.1

First, use the positive value of the $\pm$ to find the first solution.

$2 y = x$

Step 3.2

Divide each term in $2 y = x$ by $2$ and simplify.

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Step 3.2.1

Divide each term in $2 y = x$ by $2$ .

$\frac{2 y}{2} = \frac{x}{2}$

Step 3.2.2

Simplify the left side.

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Step 3.2.2.1

Cancel the common factor of $2$ .

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Step 3.2.2.1.1

Cancel the common factor.

$\frac{2 y}{2} = \frac{x}{2}$

Step 3.2.2.1.2

Divide $y$ by $1$ .

$y = \frac{x}{2}$

Step 3.3

Next, use the negative value of the $\pm$ to find the second solution.

$2 y = - x$

Step 3.4

Divide each term in $2 y = - x$ by $2$ and simplify.

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Step 3.4.1

Divide each term in $2 y = - x$ by $2$ .

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

Step 3.4.2

Simplify the left side.

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Step 3.4.2.1

Cancel the common factor of $2$ .

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Step 3.4.2.1.1

Cancel the common factor.

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

Step 3.4.2.1.2

Divide $y$ by $1$ .

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

Step 3.4.3

Simplify the right side.

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Step 3.4.3.1

Move the negative in front of the fraction.

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

Step 3.5

The complete solution is the result of both the positive and negative portions of the solution.

$y = \frac{x}{2}$

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

$y = \frac{x}{2}$

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