Basic Math Examples

$\frac{2}{3} v + \frac{1}{6} = \frac{7}{9} v - \frac{5}{6}$

Step 1

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

$\frac{2 v}{3} + \frac{1}{6} = \frac{7}{9} v - \frac{5}{6}$

Step 2

Combine $\frac{7}{9}$ and $v$ .

$\frac{2 v}{3} + \frac{1}{6} = \frac{7 v}{9} - \frac{5}{6}$

Step 3

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

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Step 3.1

Subtract $\frac{7 v}{9}$ from both sides of the equation.

$\frac{2 v}{3} + \frac{1}{6} - \frac{7 v}{9} = - \frac{5}{6}$

Step 3.2

To write $\frac{2 v}{3}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{2 v}{3} \cdot \frac{3}{3} - \frac{7 v}{9} + \frac{1}{6} = - \frac{5}{6}$

Step 3.3

Write each expression with a common denominator of $9$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.3.1

Multiply $\frac{2 v}{3}$ by $\frac{3}{3}$ .

$\frac{2 v \cdot 3}{3 \cdot 3} - \frac{7 v}{9} + \frac{1}{6} = - \frac{5}{6}$

Step 3.3.2

Multiply $3$ by $3$ .

$\frac{2 v \cdot 3}{9} - \frac{7 v}{9} + \frac{1}{6} = - \frac{5}{6}$

Step 3.4

Combine the numerators over the common denominator.

$\frac{2 v \cdot 3 - 7 v}{9} + \frac{1}{6} = - \frac{5}{6}$

Step 3.5

Simplify each term.

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Step 3.5.1

Simplify the numerator.

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Step 3.5.1.1

Factor $v$ out of $2 v \cdot 3 - 7 v$ .

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Step 3.5.1.1.1

Factor $v$ out of $2 v \cdot 3$ .

$\frac{v (2 \cdot 3) - 7 v}{9} + \frac{1}{6} = - \frac{5}{6}$

Step 3.5.1.1.2

Factor $v$ out of $- 7 v$ .

$\frac{v (2 \cdot 3) + v \cdot - 7}{9} + \frac{1}{6} = - \frac{5}{6}$

Step 3.5.1.1.3

Factor $v$ out of $v (2 \cdot 3) + v \cdot - 7$ .

$\frac{v (2 \cdot 3 - 7)}{9} + \frac{1}{6} = - \frac{5}{6}$

Step 3.5.1.2

Multiply $2$ by $3$ .

$\frac{v (6 - 7)}{9} + \frac{1}{6} = - \frac{5}{6}$

Step 3.5.1.3

Subtract $7$ from $6$ .

$\frac{v \cdot - 1}{9} + \frac{1}{6} = - \frac{5}{6}$

Step 3.5.2

Move $- 1$ to the left of $v$ .

$\frac{- 1 \cdot v}{9} + \frac{1}{6} = - \frac{5}{6}$

Step 3.5.3

Move the negative in front of the fraction.

$- \frac{v}{9} + \frac{1}{6} = - \frac{5}{6}$

Step 4

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

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Step 4.1

Subtract $\frac{1}{6}$ from both sides of the equation.

$- \frac{v}{9} = - \frac{5}{6} - \frac{1}{6}$

Step 4.2

Combine the numerators over the common denominator.

$- \frac{v}{9} = \frac{- 5 - 1}{6}$

Step 4.3

Subtract $1$ from $- 5$ .

$- \frac{v}{9} = \frac{- 6}{6}$

Step 4.4

Divide $- 6$ by $6$ .

$- \frac{v}{9} = - 1$

Step 5

Multiply both sides of the equation by $- 9$ .

$- 9 (- \frac{v}{9}) = - 9 \cdot - 1$

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 $- 9 (- \frac{v}{9})$ .

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Step 6.1.1.1

Cancel the common factor of $9$ .

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Step 6.1.1.1.1

Move the leading negative in $- \frac{v}{9}$ into the numerator.

$- 9 \frac{- v}{9} = - 9 \cdot - 1$

Step 6.1.1.1.2

Factor $9$ out of $- 9$ .

$9 (- 1) \frac{- v}{9} = - 9 \cdot - 1$

Step 6.1.1.1.3

Cancel the common factor.

$9 \cdot - 1 \frac{- v}{9} = - 9 \cdot - 1$

Step 6.1.1.1.4

Rewrite the expression.

$- - v = - 9 \cdot - 1$

Step 6.1.1.2

Multiply.

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Step 6.1.1.2.1

Multiply $- 1$ by $- 1$ .

$1 v = - 9 \cdot - 1$

Step 6.1.1.2.2

Multiply $v$ by $1$ .

$v = - 9 \cdot - 1$

Step 6.2

Simplify the right side.

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Step 6.2.1

Multiply $- 9$ by $- 1$ .

$v = 9$