Basic Math Examples

$| 3 w | = 12$

Step 1

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

$3 w = \pm 12$

Step 2

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

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Step 2.1

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

$3 w = 12$

Step 2.2

Divide each term in $3 w = 12$ by $3$ and simplify.

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Step 2.2.1

Divide each term in $3 w = 12$ by $3$ .

$\frac{3 w}{3} = \frac{12}{3}$

Step 2.2.2

Simplify the left side.

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Step 2.2.2.1

Cancel the common factor of $3$ .

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Step 2.2.2.1.1

Cancel the common factor.

$\frac{3 w}{3} = \frac{12}{3}$

Step 2.2.2.1.2

Divide $w$ by $1$ .

$w = \frac{12}{3}$

Step 2.2.3

Simplify the right side.

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Step 2.2.3.1

Divide $12$ by $3$ .

$w = 4$

Step 2.3

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

$3 w = - 12$

Step 2.4

Divide each term in $3 w = - 12$ by $3$ and simplify.

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Step 2.4.1

Divide each term in $3 w = - 12$ by $3$ .

$\frac{3 w}{3} = \frac{- 12}{3}$

Step 2.4.2

Simplify the left side.

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Step 2.4.2.1

Cancel the common factor of $3$ .

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Step 2.4.2.1.1

Cancel the common factor.

$\frac{3 w}{3} = \frac{- 12}{3}$

Step 2.4.2.1.2

Divide $w$ by $1$ .

$w = \frac{- 12}{3}$

Step 2.4.3

Simplify the right side.

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Step 2.4.3.1

Divide $- 12$ by $3$ .

$w = - 4$

Step 2.5

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

$w = 4, - 4$