Algebra Examples

$| 3 (x - 2) | = 12$

Step 1

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

$3 (x - 2) = \pm 12$

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.

$3 (x - 2) = 12$

Step 2.2

Divide each term in $3 (x - 2) = 12$ by $3$ and simplify.

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Step 2.2.1

Divide each term in $3 (x - 2) = 12$ by $3$ .

$\frac{3 (x - 2)}{3} = \frac{12}{3}$

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.

$\frac{3 (x - 2)}{3} = \frac{12}{3}$

Step 2.2.2.1.2

Divide $x - 2$ by $1$ .

$x - 2 = \frac{12}{3}$

Step 2.2.3

Simplify the right side.

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Step 2.2.3.1

Divide $12$ by $3$ .

$x - 2 = 4$

Step 2.3

Move all terms not containing $x$ to the right side of the equation.

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Step 2.3.1

Add $2$ to both sides of the equation.

$x = 4 + 2$

Step 2.3.2

Add $4$ and $2$ .

$x = 6$

Step 2.4

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

$3 (x - 2) = - 12$

Step 2.5

Divide each term in $3 (x - 2) = - 12$ by $3$ and simplify.

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Step 2.5.1

Divide each term in $3 (x - 2) = - 12$ by $3$ .

$\frac{3 (x - 2)}{3} = \frac{- 12}{3}$

Step 2.5.2

Simplify the left side.

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Step 2.5.2.1

Cancel the common factor of $3$ .

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Step 2.5.2.1.1

Cancel the common factor.

$\frac{3 (x - 2)}{3} = \frac{- 12}{3}$

Step 2.5.2.1.2

Divide $x - 2$ by $1$ .

$x - 2 = \frac{- 12}{3}$

Step 2.5.3

Simplify the right side.

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Step 2.5.3.1

Divide $- 12$ by $3$ .

$x - 2 = - 4$

Step 2.6

Move all terms not containing $x$ to the right side of the equation.

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Step 2.6.1

Add $2$ to both sides of the equation.

$x = - 4 + 2$

Step 2.6.2

Add $- 4$ and $2$ .

$x = - 2$

Step 2.7

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

$x = 6, - 2$