Basic Math Examples

$\frac{- 1}{3} v - \frac{7}{3} = 7 v - \frac{1}{2}$

Step 1

Simplify each term.

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Step 1.1

Move the negative in front of the fraction.

$- \frac{1}{3} v - \frac{7}{3} = 7 v - \frac{1}{2}$

Step 1.2

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

$- \frac{v}{3} - \frac{7}{3} = 7 v - \frac{1}{2}$

Step 2

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

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Step 2.1

Subtract $7 v$ from both sides of the equation.

$- \frac{v}{3} - \frac{7}{3} - 7 v = - \frac{1}{2}$

Step 2.2

To write $- 7 v$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$- \frac{v}{3} - 7 v \cdot \frac{3}{3} - \frac{7}{3} = - \frac{1}{2}$

Step 2.3

Combine $- 7 v$ and $\frac{3}{3}$ .

$- \frac{v}{3} + \frac{- 7 v \cdot 3}{3} - \frac{7}{3} = - \frac{1}{2}$

Step 2.4

Combine the numerators over the common denominator.

$\frac{- v - 7 v \cdot 3}{3} - \frac{7}{3} = - \frac{1}{2}$

Step 2.5

Combine the numerators over the common denominator.

$\frac{- v - 7 v \cdot 3 - 7}{3} = - \frac{1}{2}$

Step 2.6

Multiply $3$ by $- 7$ .

$\frac{- v - 21 v - 7}{3} = - \frac{1}{2}$

Step 2.7

Subtract $21 v$ from $- v$ .

$\frac{- 22 v - 7}{3} = - \frac{1}{2}$

Step 2.8

Factor $- 1$ out of $- 22 v$ .

$\frac{- (22 v) - 7}{3} = - \frac{1}{2}$

Step 2.9

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

$\frac{- (22 v) - 1 (7)}{3} = - \frac{1}{2}$

Step 2.10

Factor $- 1$ out of $- (22 v) - 1 (7)$ .

$\frac{- (22 v + 7)}{3} = - \frac{1}{2}$

Step 2.11

Rewrite $- (22 v + 7)$ as $- 1 (22 v + 7)$ .

$\frac{- 1 (22 v + 7)}{3} = - \frac{1}{2}$

Step 2.12

Move the negative in front of the fraction.

$- \frac{22 v + 7}{3} = - \frac{1}{2}$

Step 3

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

$- 3 (- \frac{22 v + 7}{3}) = - 3 (- \frac{1}{2})$

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

Simplify $- 3 (- \frac{22 v + 7}{3})$ .

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Step 4.1.1.1

Cancel the common factor of $3$ .

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Step 4.1.1.1.1

Move the leading negative in $- \frac{22 v + 7}{3}$ into the numerator.

$- 3 \frac{- (22 v + 7)}{3} = - 3 (- \frac{1}{2})$

Step 4.1.1.1.2

Factor $3$ out of $- 3$ .

$3 (- 1) \frac{- (22 v + 7)}{3} = - 3 (- \frac{1}{2})$

Step 4.1.1.1.3

Cancel the common factor.

$3 \cdot - 1 \frac{- (22 v + 7)}{3} = - 3 (- \frac{1}{2})$

Step 4.1.1.1.4

Rewrite the expression.

$- - (22 v + 7) = - 3 (- \frac{1}{2})$

Step 4.1.1.2

Multiply.

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Step 4.1.1.2.1

Multiply $- 1$ by $- 1$ .

$1 (22 v + 7) = - 3 (- \frac{1}{2})$

Step 4.1.1.2.2

Multiply $22 v + 7$ by $1$ .

$22 v + 7 = - 3 (- \frac{1}{2})$

Step 4.2

Simplify the right side.

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Step 4.2.1

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

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Step 4.2.1.1

Multiply $- 1$ by $- 3$ .

$22 v + 7 = 3 (\frac{1}{2})$

Step 4.2.1.2

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

$22 v + 7 = \frac{3}{2}$

Step 5

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

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Step 5.1

Subtract $7$ from both sides of the equation.

$22 v = \frac{3}{2} - 7$

Step 5.2

To write $- 7$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$22 v = \frac{3}{2} - 7 \cdot \frac{2}{2}$

Step 5.3

Combine $- 7$ and $\frac{2}{2}$ .

$22 v = \frac{3}{2} + \frac{- 7 \cdot 2}{2}$

Step 5.4

Combine the numerators over the common denominator.

$22 v = \frac{3 - 7 \cdot 2}{2}$

Step 5.5

Simplify the numerator.

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Step 5.5.1

Multiply $- 7$ by $2$ .

$22 v = \frac{3 - 14}{2}$

Step 5.5.2

Subtract $14$ from $3$ .

$22 v = \frac{- 11}{2}$

Step 5.6

Move the negative in front of the fraction.

$22 v = - \frac{11}{2}$

Step 6

Divide each term in $22 v = - \frac{11}{2}$ by $22$ and simplify.

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Step 6.1

Divide each term in $22 v = - \frac{11}{2}$ by $22$ .

$\frac{22 v}{22} = \frac{- \frac{11}{2}}{22}$

Step 6.2

Simplify the left side.

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Step 6.2.1

Cancel the common factor of $22$ .

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Step 6.2.1.1

Cancel the common factor.

$\frac{22 v}{22} = \frac{- \frac{11}{2}}{22}$

Step 6.2.1.2

Divide $v$ by $1$ .

$v = \frac{- \frac{11}{2}}{22}$

Step 6.3

Simplify the right side.

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Step 6.3.1

Multiply the numerator by the reciprocal of the denominator.

$v = - \frac{11}{2} \cdot \frac{1}{22}$

Step 6.3.2

Cancel the common factor of $11$ .

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Step 6.3.2.1

Move the leading negative in $- \frac{11}{2}$ into the numerator.

$v = \frac{- 11}{2} \cdot \frac{1}{22}$

Step 6.3.2.2

Factor $11$ out of $- 11$ .

$v = \frac{11 (- 1)}{2} \cdot \frac{1}{22}$

Step 6.3.2.3

Factor $11$ out of $22$ .

$v = \frac{11 \cdot - 1}{2} \cdot \frac{1}{11 \cdot 2}$

Step 6.3.2.4

Cancel the common factor.

$v = \frac{11 \cdot - 1}{2} \cdot \frac{1}{11 \cdot 2}$

Step 6.3.2.5

Rewrite the expression.

$v = \frac{- 1}{2} \cdot \frac{1}{2}$

Step 6.3.3

Multiply $\frac{- 1}{2}$ by $\frac{1}{2}$ .

$v = \frac{- 1}{2 \cdot 2}$

Step 6.3.4

Simplify the expression.

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Step 6.3.4.1

Multiply $2$ by $2$ .

$v = \frac{- 1}{4}$

Step 6.3.4.2

Move the negative in front of the fraction.

$v = - \frac{1}{4}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$v = - \frac{1}{4}$

Decimal Form:

$v = - 0.25$