Pre-Algebra Examples

$\frac{5 v}{v + 7} - 5 = \frac{7 v}{v + 7}$

Step 1

Simplify $\frac{5 v}{v + 7} - 5$ .

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Step 1.1

To write $- 5$ as a fraction with a common denominator, multiply by $\frac{v + 7}{v + 7}$ .

$\frac{5 v}{v + 7} - 5 \cdot \frac{v + 7}{v + 7} = \frac{7 v}{v + 7}$

Step 1.2

Simplify terms.

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Step 1.2.1

Combine $- 5$ and $\frac{v + 7}{v + 7}$ .

$\frac{5 v}{v + 7} + \frac{- 5 (v + 7)}{v + 7} = \frac{7 v}{v + 7}$

Step 1.2.2

Combine the numerators over the common denominator.

$\frac{5 v - 5 (v + 7)}{v + 7} = \frac{7 v}{v + 7}$

Step 1.3

Simplify the numerator.

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Step 1.3.1

Factor $5$ out of $5 v - 5 (v + 7)$ .

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Step 1.3.1.1

Factor $5$ out of $5 v$ .

$\frac{5 (v) - 5 (v + 7)}{v + 7} = \frac{7 v}{v + 7}$

Step 1.3.1.2

Factor $5$ out of $- 5 (v + 7)$ .

$\frac{5 (v) + 5 (- (v + 7))}{v + 7} = \frac{7 v}{v + 7}$

Step 1.3.1.3

Factor $5$ out of $5 (v) + 5 (- (v + 7))$ .

$\frac{5 (v - (v + 7))}{v + 7} = \frac{7 v}{v + 7}$

Step 1.3.2

Apply the distributive property.

$\frac{5 (v - v - 1 \cdot 7)}{v + 7} = \frac{7 v}{v + 7}$

Step 1.3.3

Multiply $- 1$ by $7$ .

$\frac{5 (v - v - 7)}{v + 7} = \frac{7 v}{v + 7}$

Step 1.3.4

Subtract $v$ from $v$ .

$\frac{5 (0 - 7)}{v + 7} = \frac{7 v}{v + 7}$

Step 1.3.5

Subtract $7$ from $0$ .

$\frac{5 \cdot - 7}{v + 7} = \frac{7 v}{v + 7}$

Step 1.4

Simplify the expression.

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Step 1.4.1

Multiply $5$ by $- 7$ .

$\frac{- 35}{v + 7} = \frac{7 v}{v + 7}$

Step 1.4.2

Move the negative in front of the fraction.

$- \frac{35}{v + 7} = \frac{7 v}{v + 7}$

Step 2

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

$v = - 5$

Step 3