Basic Math Examples

$27 = \frac{1}{2} \cdot (3 m - 2 w)$

Step 1

Rewrite the equation as $\frac{1}{2} \cdot (3 m - 2 w) = 27$ .

$\frac{1}{2} \cdot (3 m - 2 w) = 27$

Step 2

Multiply both sides of the equation by $2$ .

$2 (\frac{1}{2} \cdot (3 m - 2 w)) = 2 \cdot 27$

Step 3

Simplify both sides of the equation.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Simplify $2 (\frac{1}{2} \cdot (3 m - 2 w))$ .

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Step 3.1.1.1

Apply the distributive property.

$2 (\frac{1}{2} (3 m) + \frac{1}{2} (- 2 w)) = 2 \cdot 27$

Step 3.1.1.2

Multiply $\frac{1}{2} (3 m)$ .

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Step 3.1.1.2.1

Combine $3$ and $\frac{1}{2}$ .

$2 (\frac{3}{2} m + \frac{1}{2} (- 2 w)) = 2 \cdot 27$

Step 3.1.1.2.2

Combine $\frac{3}{2}$ and $m$ .

$2 (\frac{3 m}{2} + \frac{1}{2} (- 2 w)) = 2 \cdot 27$

Step 3.1.1.3

Cancel the common factor of $2$ .

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Step 3.1.1.3.1

Factor $2$ out of $- 2 w$ .

$2 (\frac{3 m}{2} + \frac{1}{2} (2 (- w))) = 2 \cdot 27$

Step 3.1.1.3.2

Cancel the common factor.

$2 (\frac{3 m}{2} + \frac{1}{2} (2 (- w))) = 2 \cdot 27$

Step 3.1.1.3.3

Rewrite the expression.

$2 (\frac{3 m}{2} - w) = 2 \cdot 27$

Step 3.1.1.4

Apply the distributive property.

$2 \frac{3 m}{2} + 2 (- w) = 2 \cdot 27$

Step 3.1.1.5

Cancel the common factor of $2$ .

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Step 3.1.1.5.1

Cancel the common factor.

$2 \frac{3 m}{2} + 2 (- w) = 2 \cdot 27$

Step 3.1.1.5.2

Rewrite the expression.

$3 m + 2 (- w) = 2 \cdot 27$

Step 3.1.1.6

Multiply $- 1$ by $2$ .

$3 m - 2 w = 2 \cdot 27$

Step 3.2

Simplify the right side.

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Step 3.2.1

Multiply $2$ by $27$ .

$3 m - 2 w = 54$

Step 4

Subtract $3 m$ from both sides of the equation.

$- 2 w = 54 - 3 m$

Step 5

Divide each term in $- 2 w = 54 - 3 m$ by $- 2$ and simplify.

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Step 5.1

Divide each term in $- 2 w = 54 - 3 m$ by $- 2$ .

$\frac{- 2 w}{- 2} = \frac{54}{- 2} + \frac{- 3 m}{- 2}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $- 2$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{- 2 w}{- 2} = \frac{54}{- 2} + \frac{- 3 m}{- 2}$

Step 5.2.1.2

Divide $w$ by $1$ .

$w = \frac{54}{- 2} + \frac{- 3 m}{- 2}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Simplify each term.

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Step 5.3.1.1

Divide $54$ by $- 2$ .

$w = - 27 + \frac{- 3 m}{- 2}$

Step 5.3.1.2

Dividing two negative values results in a positive value.

$w = - 27 + \frac{3 m}{2}$