Basic Math Examples

$- \frac{7}{3} v - \frac{1}{5} = \frac{4}{3} v - 4$

Step 1

Simplify each term.

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Step 1.1

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

$- \frac{v \cdot 7}{3} - \frac{1}{5} = \frac{4}{3} v - 4$

Step 1.2

Move $7$ to the left of $v$ .

$- \frac{7 v}{3} - \frac{1}{5} = \frac{4}{3} v - 4$

Step 2

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

$- \frac{7 v}{3} - \frac{1}{5} = \frac{4 v}{3} - 4$

Step 3

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

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Step 3.1

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

$- \frac{7 v}{3} - \frac{1}{5} - \frac{4 v}{3} = - 4$

Step 3.2

Combine the numerators over the common denominator.

$\frac{- 7 v - 4 v}{3} + \frac{- 1}{5} = - 4$

Step 3.3

Subtract $4 v$ from $- 7 v$ .

$\frac{- 11 v}{3} + \frac{- 1}{5} = - 4$

Step 3.4

Simplify each term.

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Step 3.4.1

Move the negative in front of the fraction.

$- \frac{11 v}{3} + \frac{- 1}{5} = - 4$

Step 3.4.2

Move the negative in front of the fraction.

$- \frac{11 v}{3} - \frac{1}{5} = - 4$

Step 4

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

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Step 4.1

Add $\frac{1}{5}$ to both sides of the equation.

$- \frac{11 v}{3} = - 4 + \frac{1}{5}$

Step 4.2

To write $- 4$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$- \frac{11 v}{3} = - 4 \cdot \frac{5}{5} + \frac{1}{5}$

Step 4.3

Combine $- 4$ and $\frac{5}{5}$ .

$- \frac{11 v}{3} = \frac{- 4 \cdot 5}{5} + \frac{1}{5}$

Step 4.4

Combine the numerators over the common denominator.

$- \frac{11 v}{3} = \frac{- 4 \cdot 5 + 1}{5}$

Step 4.5

Simplify the numerator.

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Step 4.5.1

Multiply $- 4$ by $5$ .

$- \frac{11 v}{3} = \frac{- 20 + 1}{5}$

Step 4.5.2

Add $- 20$ and $1$ .

$- \frac{11 v}{3} = \frac{- 19}{5}$

Step 4.6

Move the negative in front of the fraction.

$- \frac{11 v}{3} = - \frac{19}{5}$

Step 5

Multiply both sides of the equation by $- \frac{3}{11}$ .

$- \frac{3}{11} (- \frac{11 v}{3}) = - \frac{3}{11} (- \frac{19}{5})$

Step 6

Simplify both sides of the equation.

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Step 6.1

Simplify the left side.

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Step 6.1.1

Simplify $- \frac{3}{11} (- \frac{11 v}{3})$ .

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Step 6.1.1.1

Cancel the common factor of $3$ .

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Step 6.1.1.1.1

Move the leading negative in $- \frac{3}{11}$ into the numerator.

$\frac{- 3}{11} (- \frac{11 v}{3}) = - \frac{3}{11} (- \frac{19}{5})$

Step 6.1.1.1.2

Move the leading negative in $- \frac{11 v}{3}$ into the numerator.

$\frac{- 3}{11} \cdot \frac{- 11 v}{3} = - \frac{3}{11} (- \frac{19}{5})$

Step 6.1.1.1.3

Factor $3$ out of $- 3$ .

$\frac{3 (- 1)}{11} \cdot \frac{- 11 v}{3} = - \frac{3}{11} (- \frac{19}{5})$

Step 6.1.1.1.4

Cancel the common factor.

$\frac{3 \cdot - 1}{11} \cdot \frac{- 11 v}{3} = - \frac{3}{11} (- \frac{19}{5})$

Step 6.1.1.1.5

Rewrite the expression.

$\frac{- 1}{11} (- 11 v) = - \frac{3}{11} (- \frac{19}{5})$

Step 6.1.1.2

Cancel the common factor of $11$ .

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Step 6.1.1.2.1

Factor $11$ out of $- 11 v$ .

$\frac{- 1}{11} (11 (- v)) = - \frac{3}{11} (- \frac{19}{5})$

Step 6.1.1.2.2

Cancel the common factor.

$\frac{- 1}{11} (11 (- v)) = - \frac{3}{11} (- \frac{19}{5})$

Step 6.1.1.2.3

Rewrite the expression.

$- - v = - \frac{3}{11} (- \frac{19}{5})$

Step 6.1.1.3

Multiply.

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Step 6.1.1.3.1

Multiply $- 1$ by $- 1$ .

$1 v = - \frac{3}{11} (- \frac{19}{5})$

Step 6.1.1.3.2

Multiply $v$ by $1$ .

$v = - \frac{3}{11} (- \frac{19}{5})$

Step 6.2

Simplify the right side.

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Step 6.2.1

Multiply $- \frac{3}{11} (- \frac{19}{5})$ .

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Step 6.2.1.1

Multiply $- 1$ by $- 1$ .

$v = 1 (\frac{3}{11}) \frac{19}{5}$

Step 6.2.1.2

Multiply $\frac{3}{11}$ by $1$ .

$v = \frac{3}{11} \cdot \frac{19}{5}$

Step 6.2.1.3

Multiply $\frac{3}{11}$ by $\frac{19}{5}$ .

$v = \frac{3 \cdot 19}{11 \cdot 5}$

Step 6.2.1.4

Multiply $3$ by $19$ .

$v = \frac{57}{11 \cdot 5}$

Step 6.2.1.5

Multiply $11$ by $5$ .

$v = \frac{57}{55}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$v = \frac{57}{55}$

Decimal Form:

$v = 1.0\overline{36}$

Mixed Number Form:

$v = 1 \frac{2}{55}$