Basic Math Examples

| 3 n - 3 | = 6

$| 3 n - 3 | = 6$

Step 1

Remove the absolute value term. This creates a

\pm

$\pm$ on the right side of the equation because

| x | = \pm x

$| x | = \pm x$ .

3 n - 3 = \pm 6

$3 n - 3 = \pm 6$

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

$\pm$ to find the first solution.

3 n - 3 = 6

$3 n - 3 = 6$

Step 2.2

Move all terms not containing

n

$n$ to the right side of the equation.

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Step 2.2.1

Add

3

$3$ to both sides of the equation.

3 n = 6 + 3

$3 n = 6 + 3$

Step 2.2.2

Add

6

$6$ and

3

$3$ .

3 n = 9

$3 n = 9$

3 n = 9

$3 n = 9$

Step 2.3

Divide each term in

3 n = 9

$3 n = 9$ by

3

$3$ and simplify.

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Step 2.3.1

Divide each term in

3 n = 9

$3 n = 9$ by

3

$3$ .

\frac{3 n}{3} = \frac{9}{3}

$\frac{3 n}{3} = \frac{9}{3}$

Step 2.3.2

Simplify the left side.

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Step 2.3.2.1

Cancel the common factor of

3

$3$ .

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Step 2.3.2.1.1

Cancel the common factor.

$\frac{3 n}{3} = \frac{9}{3}$

Step 2.3.2.1.2

Divide

$n$ by

$1$ .

$n = \frac{9}{3}$

Step 2.3.3

Simplify the right side.

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Step 2.3.3.1

Divide

$9$ by

$3$ .

$n = 3$

Step 2.4

Next, use the negative value of the

$\pm$ to find the second solution.

$3 n - 3 = - 6$

Step 2.5

Move all terms not containing

$n$ to the right side of the equation.

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Step 2.5.1

Add

$3$ to both sides of the equation.

$3 n = - 6 + 3$

Step 2.5.2

Add

$- 6$ and

$3$ .

$3 n = - 3$

Step 2.6

Divide each term in

$3 n = - 3$ by

$3$ and simplify.

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Step 2.6.1

Divide each term in

$3 n = - 3$ by

$3$ .

$\frac{3 n}{3} = \frac{- 3}{3}$

Step 2.6.2

Simplify the left side.

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Step 2.6.2.1

Cancel the common factor of

$3$ .

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Step 2.6.2.1.1

Cancel the common factor.

$\frac{3 n}{3} = \frac{- 3}{3}$

Step 2.6.2.1.2

Divide

$n$ by

$1$ .

$n = \frac{- 3}{3}$

Step 2.6.3

Simplify the right side.

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Step 2.6.3.1

Divide

$- 3$ by

$3$ .

$n = - 1$

Step 2.7

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

$n = 3, - 1$