Algebra Examples

$g = \frac{1}{6} (w + 40)$

Step 1

Rewrite the equation as $\frac{1}{6} \cdot (w + 40) = g$ .

$\frac{1}{6} \cdot (w + 40) = g$

Step 2

Multiply both sides of the equation by $6$ .

$6 (\frac{1}{6} \cdot (w + 40)) = 6 g$

Step 3

Simplify the left side.

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Step 3.1

Simplify $6 (\frac{1}{6} \cdot (w + 40))$ .

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Step 3.1.1

Apply the distributive property.

$6 (\frac{1}{6} w + \frac{1}{6} \cdot 40) = 6 g$

Step 3.1.2

Combine $\frac{1}{6}$ and $w$ .

$6 (\frac{w}{6} + \frac{1}{6} \cdot 40) = 6 g$

Step 3.1.3

Cancel the common factor of $2$ .

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Step 3.1.3.1

Factor $2$ out of $6$ .

$6 (\frac{w}{6} + \frac{1}{2 (3)} \cdot 40) = 6 g$

Step 3.1.3.2

Factor $2$ out of $40$ .

$6 (\frac{w}{6} + \frac{1}{2 \cdot 3} \cdot (2 \cdot 20)) = 6 g$

Step 3.1.3.3

Cancel the common factor.

$6 (\frac{w}{6} + \frac{1}{2 \cdot 3} \cdot (2 \cdot 20)) = 6 g$

Step 3.1.3.4

Rewrite the expression.

$6 (\frac{w}{6} + \frac{1}{3} \cdot 20) = 6 g$

Step 3.1.4

Combine $\frac{1}{3}$ and $20$ .

$6 (\frac{w}{6} + \frac{20}{3}) = 6 g$

Step 3.1.5

Apply the distributive property.

$6 \frac{w}{6} + 6 (\frac{20}{3}) = 6 g$

Step 3.1.6

Cancel the common factor of $6$ .

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Step 3.1.6.1

Cancel the common factor.

$6 \frac{w}{6} + 6 (\frac{20}{3}) = 6 g$

Step 3.1.6.2

Rewrite the expression.

$w + 6 (\frac{20}{3}) = 6 g$

Step 3.1.7

Cancel the common factor of $3$ .

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Step 3.1.7.1

Factor $3$ out of $6$ .

$w + 3 (2) \frac{20}{3} = 6 g$

Step 3.1.7.2

Cancel the common factor.

$w + 3 \cdot 2 \frac{20}{3} = 6 g$

Step 3.1.7.3

Rewrite the expression.

$w + 2 \cdot 20 = 6 g$

Step 3.1.8

Multiply $2$ by $20$ .

$w + 40 = 6 g$

Step 4

Subtract $40$ from both sides of the equation.

$w = 6 g - 40$