Basic Math Examples

$\frac{w}{4} = \frac{w}{3} - 3$

Step 1

Multiply both sides by $4$ .

$\frac{w}{4} \cdot 4 = (\frac{w}{3} - 3) \cdot 4$

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Cancel the common factor of $4$ .

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Step 2.1.1.1

Cancel the common factor.

$\frac{w}{4} \cdot 4 = (\frac{w}{3} - 3) \cdot 4$

Step 2.1.1.2

Rewrite the expression.

$w = (\frac{w}{3} - 3) \cdot 4$

Step 2.2

Simplify the right side.

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Step 2.2.1

Simplify $(\frac{w}{3} - 3) \cdot 4$ .

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Step 2.2.1.1

Simplify terms.

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Step 2.2.1.1.1

Apply the distributive property.

$w = \frac{w}{3} \cdot 4 - 3 \cdot 4$

Step 2.2.1.1.2

Combine $\frac{w}{3}$ and $4$ .

$w = \frac{w \cdot 4}{3} - 3 \cdot 4$

Step 2.2.1.1.3

Multiply $- 3$ by $4$ .

$w = \frac{w \cdot 4}{3} - 12$

Step 2.2.1.2

Move $4$ to the left of $w$ .

$w = \frac{4 w}{3} - 12$

Step 3

Solve for $w$ .

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Step 3.1

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

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Step 3.1.1

Subtract $\frac{4 w}{3}$ from both sides of the equation.

$w - \frac{4 w}{3} = - 12$

Step 3.1.2

To write $w$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$w \cdot \frac{3}{3} - \frac{4 w}{3} = - 12$

Step 3.1.3

Combine $w$ and $\frac{3}{3}$ .

$\frac{w \cdot 3}{3} - \frac{4 w}{3} = - 12$

Step 3.1.4

Combine the numerators over the common denominator.

$\frac{w \cdot 3 - 4 w}{3} = - 12$

Step 3.1.5

Simplify the numerator.

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Step 3.1.5.1

Move $3$ to the left of $w$ .

$\frac{3 \cdot w - 4 w}{3} = - 12$

Step 3.1.5.2

Subtract $4 w$ from $3 w$ .

$\frac{- w}{3} = - 12$

Step 3.1.6

Move the negative in front of the fraction.

$- \frac{w}{3} = - 12$

Step 3.2

Multiply both sides of the equation by $- 3$ .

$- 3 (- \frac{w}{3}) = - 3 \cdot - 12$

Step 3.3

Simplify both sides of the equation.

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Step 3.3.1

Simplify the left side.

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Step 3.3.1.1

Simplify $- 3 (- \frac{w}{3})$ .

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Step 3.3.1.1.1

Cancel the common factor of $3$ .

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Step 3.3.1.1.1.1

Move the leading negative in $- \frac{w}{3}$ into the numerator.

$- 3 \frac{- w}{3} = - 3 \cdot - 12$

Step 3.3.1.1.1.2

Factor $3$ out of $- 3$ .

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

Step 3.3.1.1.1.3

Cancel the common factor.

$3 \cdot - 1 \frac{- w}{3} = - 3 \cdot - 12$

Step 3.3.1.1.1.4

Rewrite the expression.

$- - w = - 3 \cdot - 12$

Step 3.3.1.1.2

Multiply.

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Step 3.3.1.1.2.1

Multiply $- 1$ by $- 1$ .

$1 w = - 3 \cdot - 12$

Step 3.3.1.1.2.2

Multiply $w$ by $1$ .

$w = - 3 \cdot - 12$

Step 3.3.2

Simplify the right side.

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Step 3.3.2.1

Multiply $- 3$ by $- 12$ .

$w = 36$