Pre-Algebra Examples

$8 - 4 w = \frac{1}{3} \cdot (6 w - 12)$

Step 1

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

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Step 1.1

Rewrite.

$8 - 4 w = 0 + 0 + \frac{1}{3} \cdot (6 w - 12)$

Step 1.2

Simplify by adding zeros.

$8 - 4 w = \frac{1}{3} \cdot (6 w - 12)$

Step 1.3

Apply the distributive property.

$8 - 4 w = \frac{1}{3} (6 w) + \frac{1}{3} \cdot - 12$

Step 1.4

Cancel the common factor of $3$ .

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Step 1.4.1

Factor $3$ out of $6 w$ .

$8 - 4 w = \frac{1}{3} (3 (2 w)) + \frac{1}{3} \cdot - 12$

Step 1.4.2

Cancel the common factor.

$8 - 4 w = \frac{1}{3} (3 (2 w)) + \frac{1}{3} \cdot - 12$

Step 1.4.3

Rewrite the expression.

$8 - 4 w = 2 w + \frac{1}{3} \cdot - 12$

Step 1.5

Cancel the common factor of $3$ .

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Step 1.5.1

Factor $3$ out of $- 12$ .

$8 - 4 w = 2 w + \frac{1}{3} \cdot (3 (- 4))$

Step 1.5.2

Cancel the common factor.

$8 - 4 w = 2 w + \frac{1}{3} \cdot (3 \cdot - 4)$

Step 1.5.3

Rewrite the expression.

$8 - 4 w = 2 w - 4$

Step 2

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

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Step 2.1

Subtract $2 w$ from both sides of the equation.

$8 - 4 w - 2 w = - 4$

Step 2.2

Subtract $2 w$ from $- 4 w$ .

$8 - 6 w = - 4$

Step 3

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

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Step 3.1

Subtract $8$ from both sides of the equation.

$- 6 w = - 4 - 8$

Step 3.2

Subtract $8$ from $- 4$ .

$- 6 w = - 12$

Step 4

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

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Step 4.1

Divide each term in $- 6 w = - 12$ by $- 6$ .

$\frac{- 6 w}{- 6} = \frac{- 12}{- 6}$

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.

$\frac{- 6 w}{- 6} = \frac{- 12}{- 6}$

Step 4.2.1.2

Divide $w$ by $1$ .

$w = \frac{- 12}{- 6}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Divide $- 12$ by $- 6$ .

$w = 2$