Pre-Algebra Examples

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

Step 1

Simplify $\frac{3}{4} w - \frac{1}{2} w - 4$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

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

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

Step 1.1.2

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

$\frac{3 w}{4} - \frac{w}{2} - 4 = 12$

Step 1.2

To write $- \frac{w}{2}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

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

Step 1.3

Write each expression with a common denominator of $4$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.3.1

Multiply $\frac{w}{2}$ by $\frac{2}{2}$ .

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

Step 1.3.2

Multiply $2$ by $2$ .

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

Step 1.4

Combine the numerators over the common denominator.

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

Step 1.5

Simplify each term.

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Step 1.5.1

Simplify the numerator.

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Step 1.5.1.1

Factor $w$ out of $3 w - w \cdot 2$ .

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Step 1.5.1.1.1

Factor $w$ out of $3 w$ .

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

Step 1.5.1.1.2

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

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

Step 1.5.1.1.3

Factor $w$ out of $w \cdot 3 + w (- 1 \cdot 2)$ .

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

Step 1.5.1.2

Multiply $- 1$ by $2$ .

$\frac{w (3 - 2)}{4} - 4 = 12$

Step 1.5.1.3

Subtract $2$ from $3$ .

$\frac{w \cdot 1}{4} - 4 = 12$

Step 1.5.2

Multiply $w$ by $1$ .

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

Step 2

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

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Step 2.1

Add $4$ to both sides of the equation.

$\frac{w}{4} = 12 + 4$

Step 2.2

Add $12$ and $4$ .

$\frac{w}{4} = 16$

Step 3

Multiply both sides of the equation by $4$ .

$4 \frac{w}{4} = 4 \cdot 16$

Step 4

Simplify both sides of the equation.

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Step 4.1

Simplify the left side.

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Step 4.1.1

Cancel the common factor of $4$ .

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Step 4.1.1.1

Cancel the common factor.

$4 \frac{w}{4} = 4 \cdot 16$

Step 4.1.1.2

Rewrite the expression.

$w = 4 \cdot 16$

Step 4.2

Simplify the right side.

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Step 4.2.1

Multiply $4$ by $16$ .

$w = 64$