Algebra Examples

$| 3 x | - 3 = 3 - 6 x$

Step 1

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

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Step 1.1

Add $3$ to both sides of the equation.

$| 3 x | = 3 - 6 x + 3$

Step 1.2

Add $3$ and $3$ .

$| 3 x | = - 6 x + 6$

Step 2

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

$3 x = \pm (- 6 x + 6)$

Step 3

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

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Step 3.1

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

$3 x = - 6 x + 6$

Step 3.2

Move all terms containing $x$ to the left side of the equation.

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Step 3.2.1

Add $6 x$ to both sides of the equation.

$3 x + 6 x = 6$

Step 3.2.2

Add $3 x$ and $6 x$ .

$9 x = 6$

Step 3.3

Divide each term in $9 x = 6$ by $9$ and simplify.

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Step 3.3.1

Divide each term in $9 x = 6$ by $9$ .

$\frac{9 x}{9} = \frac{6}{9}$

Step 3.3.2

Simplify the left side.

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Step 3.3.2.1

Cancel the common factor of $9$ .

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Step 3.3.2.1.1

Cancel the common factor.

$\frac{9 x}{9} = \frac{6}{9}$

Step 3.3.2.1.2

Divide $x$ by $1$ .

$x = \frac{6}{9}$

Step 3.3.3

Simplify the right side.

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Step 3.3.3.1

Cancel the common factor of $6$ and $9$ .

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Step 3.3.3.1.1

Factor $3$ out of $6$ .

$x = \frac{3 (2)}{9}$

Step 3.3.3.1.2

Cancel the common factors.

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Step 3.3.3.1.2.1

Factor $3$ out of $9$ .

$x = \frac{3 \cdot 2}{3 \cdot 3}$

Step 3.3.3.1.2.2

Cancel the common factor.

$x = \frac{3 \cdot 2}{3 \cdot 3}$

Step 3.3.3.1.2.3

Rewrite the expression.

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

Step 3.4

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

$3 x = - (- 6 x + 6)$

Step 3.5

Simplify $- (- 6 x + 6)$ .

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Step 3.5.1

Apply the distributive property.

$3 x = - (- 6 x) - 1 \cdot 6$

Step 3.5.2

Multiply.

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Step 3.5.2.1

Multiply $- 6$ by $- 1$ .

$3 x = 6 x - 1 \cdot 6$

Step 3.5.2.2

Multiply $- 1$ by $6$ .

$3 x = 6 x - 6$

Step 3.6

Move all terms containing $x$ to the left side of the equation.

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Step 3.6.1

Subtract $6 x$ from both sides of the equation.

$3 x - 6 x = - 6$

Step 3.6.2

Subtract $6 x$ from $3 x$ .

$- 3 x = - 6$

Step 3.7

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

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Step 3.7.1

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

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

Step 3.7.2

Simplify the left side.

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Step 3.7.2.1

Cancel the common factor of $- 3$ .

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Step 3.7.2.1.1

Cancel the common factor.

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

Step 3.7.2.1.2

Divide $x$ by $1$ .

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

Step 3.7.3

Simplify the right side.

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Step 3.7.3.1

Divide $- 6$ by $- 3$ .

$x = 2$

Step 3.8

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

$x = \frac{2}{3}, 2$

Step 4

Exclude the solutions that do not make $| 3 x | - 3 = 3 - 6 x$ true.

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

Step 5

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$x = 0.\overline{6}$