Algebra Examples

$3 | x | - | y | = 2$

Step 1

Add $| y |$ to both sides of the equation.

$3 | x | = 2 + | y |$

Step 2

Divide each term in $3 | x | = 2 + | y |$ by $3$ and simplify.

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Step 2.1

Divide each term in $3 | x | = 2 + | y |$ by $3$ .

$\frac{3 | x |}{3} = \frac{2}{3} + \frac{| y |}{3}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $3$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{3 | x |}{3} = \frac{2}{3} + \frac{| y |}{3}$

Step 2.2.1.2

Divide $| x |$ by $1$ .

$| x | = \frac{2}{3} + \frac{| y |}{3}$

Step 3

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

$x = \pm (\frac{2}{3} + \frac{| y |}{3})$

Step 4

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

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Step 4.1

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

$x = \frac{2}{3} + \frac{| y |}{3}$

Step 4.2

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

$x = - (\frac{2}{3} + \frac{| y |}{3})$

Step 4.3

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

$x = \frac{2}{3} + \frac{| y |}{3}$

$x = - (\frac{2}{3} + \frac{| y |}{3})$

$x = \frac{2}{3} + \frac{| y |}{3}$

$x = - (\frac{2}{3} + \frac{| y |}{3})$

Step 5