Pre-Algebra Examples

$\frac{1}{3} \cdot (6 x - 12) = 0$

Step 1

Multiply both sides of the equation by $3$ .

$3 (\frac{1}{3} \cdot (6 x - 12)) = 3 \cdot 0$

Step 2

Simplify both sides of the equation.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify $3 (\frac{1}{3} \cdot (6 x - 12))$ .

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Step 2.1.1.1

Apply the distributive property.

$3 (\frac{1}{3} (6 x) + \frac{1}{3} \cdot - 12) = 3 \cdot 0$

Step 2.1.1.2

Cancel the common factor of $3$ .

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Step 2.1.1.2.1

Factor $3$ out of $6 x$ .

$3 (\frac{1}{3} (3 (2 x)) + \frac{1}{3} \cdot - 12) = 3 \cdot 0$

Step 2.1.1.2.2

Cancel the common factor.

$3 (\frac{1}{3} (3 (2 x)) + \frac{1}{3} \cdot - 12) = 3 \cdot 0$

Step 2.1.1.2.3

Rewrite the expression.

$3 (2 x + \frac{1}{3} \cdot - 12) = 3 \cdot 0$

Step 2.1.1.3

Cancel the common factor of $3$ .

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Step 2.1.1.3.1

Factor $3$ out of $- 12$ .

$3 (2 x + \frac{1}{3} \cdot (3 (- 4))) = 3 \cdot 0$

Step 2.1.1.3.2

Cancel the common factor.

$3 (2 x + \frac{1}{3} \cdot (3 \cdot - 4)) = 3 \cdot 0$

Step 2.1.1.3.3

Rewrite the expression.

$3 (2 x - 4) = 3 \cdot 0$

Step 2.1.1.4

Apply the distributive property.

$3 (2 x) + 3 \cdot - 4 = 3 \cdot 0$

Step 2.1.1.5

Multiply.

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Step 2.1.1.5.1

Multiply $2$ by $3$ .

$6 x + 3 \cdot - 4 = 3 \cdot 0$

Step 2.1.1.5.2

Multiply $3$ by $- 4$ .

$6 x - 12 = 3 \cdot 0$

Step 2.2

Simplify the right side.

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Step 2.2.1

Multiply $3$ by $0$ .

$6 x - 12 = 0$

Step 3

Add $12$ to both sides of the equation.

$6 x = 12$

Step 4

Divide each term in $6 x = 12$ by $6$ and simplify.

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Step 4.1

Divide each term in $6 x = 12$ by $6$ .

$\frac{6 x}{6} = \frac{12}{6}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $6$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{6 x}{6} = \frac{12}{6}$

Step 4.2.1.2

Divide $x$ by $1$ .

$x = \frac{12}{6}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Divide $12$ by $6$ .

$x = 2$