Pre-Algebra Examples

$\frac{w + 2}{8 w} - \frac{3}{10} = \frac{1}{w}$

Step 1

Simplify $\frac{w + 2}{8 w} - \frac{3}{10}$ .

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Step 1.1

To write $\frac{w + 2}{8 w}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{w + 2}{8 w} \cdot \frac{5}{5} - \frac{3}{10} = \frac{1}{w}$

Step 1.2

To write $- \frac{3}{10}$ as a fraction with a common denominator, multiply by $\frac{4 w}{4 w}$ .

$\frac{w + 2}{8 w} \cdot \frac{5}{5} - \frac{3}{10} \cdot \frac{4 w}{4 w} = \frac{1}{w}$

Step 1.3

Write each expression with a common denominator of $40 w$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.3.1

Multiply $\frac{w + 2}{8 w}$ by $\frac{5}{5}$ .

$\frac{(w + 2) \cdot 5}{8 w \cdot 5} - \frac{3}{10} \cdot \frac{4 w}{4 w} = \frac{1}{w}$

Step 1.3.2

Multiply $5$ by $8$ .

$\frac{(w + 2) \cdot 5}{40 w} - \frac{3}{10} \cdot \frac{4 w}{4 w} = \frac{1}{w}$

Step 1.3.3

Multiply $\frac{3}{10}$ by $\frac{4 w}{4 w}$ .

$\frac{(w + 2) \cdot 5}{40 w} - \frac{3 (4 w)}{10 (4 w)} = \frac{1}{w}$

Step 1.3.4

Multiply $4$ by $10$ .

$\frac{(w + 2) \cdot 5}{40 w} - \frac{3 (4 w)}{40 w} = \frac{1}{w}$

Step 1.4

Combine the numerators over the common denominator.

$\frac{(w + 2) \cdot 5 - 3 (4 w)}{40 w} = \frac{1}{w}$

Step 1.5

Simplify the numerator.

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Step 1.5.1

Apply the distributive property.

$\frac{w \cdot 5 + 2 \cdot 5 - 3 \cdot 4 w}{40 w} = \frac{1}{w}$

Step 1.5.2

Move $5$ to the left of $w$ .

$\frac{5 \cdot w + 2 \cdot 5 - 3 \cdot 4 w}{40 w} = \frac{1}{w}$

Step 1.5.3

Multiply $2$ by $5$ .

$\frac{5 \cdot w + 10 - 3 \cdot 4 w}{40 w} = \frac{1}{w}$

Step 1.5.4

Multiply $- 3$ by $4$ .

$\frac{5 w + 10 - 12 w}{40 w} = \frac{1}{w}$

Step 1.5.5

Subtract $12 w$ from $5 w$ .

$\frac{- 7 w + 10}{40 w} = \frac{1}{w}$

Step 1.6

Simplify with factoring out.

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Step 1.6.1

Factor $- 1$ out of $- 7 w$ .

$\frac{- (7 w) + 10}{40 w} = \frac{1}{w}$

Step 1.6.2

Rewrite $10$ as $- 1 (- 10)$ .

$\frac{- (7 w) - 1 (- 10)}{40 w} = \frac{1}{w}$

Step 1.6.3

Factor $- 1$ out of $- (7 w) - 1 (- 10)$ .

$\frac{- (7 w - 10)}{40 w} = \frac{1}{w}$

Step 1.6.4

Simplify the expression.

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Step 1.6.4.1

Rewrite $- (7 w - 10)$ as $- 1 (7 w - 10)$ .

$\frac{- 1 (7 w - 10)}{40 w} = \frac{1}{w}$

Step 1.6.4.2

Move the negative in front of the fraction.

$- \frac{7 w - 10}{40 w} = \frac{1}{w}$

Step 2

Graph each side of the equation. The solution is the x-value of the point of intersection.

$w = - \frac{30}{7}$

Step 3