Pre-Algebra Examples

$- 2 | 3 j | - 8 = - 20$

Step 1

Move all terms not containing $| 3 j |$ to the right side of the equation.

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Step 1.1

Add $8$ to both sides of the equation.

$- 2 | 3 j | = - 20 + 8$

Step 1.2

Add $- 20$ and $8$ .

$- 2 | 3 j | = - 12$

Step 2

Divide each term in $- 2 | 3 j | = - 12$ by $- 2$ and simplify.

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Step 2.1

Divide each term in $- 2 | 3 j | = - 12$ by $- 2$ .

$\frac{- 2 | 3 j |}{- 2} = \frac{- 12}{- 2}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $- 2$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{- 2 | 3 j |}{- 2} = \frac{- 12}{- 2}$

Step 2.2.1.2

Divide $| 3 j |$ by $1$ .

$| 3 j | = \frac{- 12}{- 2}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Divide $- 12$ by $- 2$ .

$| 3 j | = 6$

Step 3

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

$3 j = \pm 6$

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.

$3 j = 6$

Step 4.2

Divide each term in $3 j = 6$ by $3$ and simplify.

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Step 4.2.1

Divide each term in $3 j = 6$ by $3$ .

$\frac{3 j}{3} = \frac{6}{3}$

Step 4.2.2

Simplify the left side.

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Step 4.2.2.1

Cancel the common factor of $3$ .

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Step 4.2.2.1.1

Cancel the common factor.

$\frac{3 j}{3} = \frac{6}{3}$

Step 4.2.2.1.2

Divide $j$ by $1$ .

$j = \frac{6}{3}$

Step 4.2.3

Simplify the right side.

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Step 4.2.3.1

Divide $6$ by $3$ .

$j = 2$

Step 4.3

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

$3 j = - 6$

Step 4.4

Divide each term in $3 j = - 6$ by $3$ and simplify.

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Step 4.4.1

Divide each term in $3 j = - 6$ by $3$ .

$\frac{3 j}{3} = \frac{- 6}{3}$

Step 4.4.2

Simplify the left side.

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Step 4.4.2.1

Cancel the common factor of $3$ .

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Step 4.4.2.1.1

Cancel the common factor.

$\frac{3 j}{3} = \frac{- 6}{3}$

Step 4.4.2.1.2

Divide $j$ by $1$ .

$j = \frac{- 6}{3}$

Step 4.4.3

Simplify the right side.

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Step 4.4.3.1

Divide $- 6$ by $3$ .

$j = - 2$

Step 4.5

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

$j = 2, - 2$