Basic Math Examples

$\frac{q}{5} + \frac{2}{5} = \frac{2 q}{7} - \frac{11}{7}$

Step 1

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

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Step 1.1

Subtract $\frac{2 q}{7}$ from both sides of the equation.

$\frac{q}{5} + \frac{2}{5} - \frac{2 q}{7} = - \frac{11}{7}$

Step 1.2

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

$\frac{q}{5} \cdot \frac{7}{7} - \frac{2 q}{7} + \frac{2}{5} = - \frac{11}{7}$

Step 1.3

To write $- \frac{2 q}{7}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{q}{5} \cdot \frac{7}{7} - \frac{2 q}{7} \cdot \frac{5}{5} + \frac{2}{5} = - \frac{11}{7}$

Step 1.4

Write each expression with a common denominator of $35$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.4.1

Multiply $\frac{q}{5}$ by $\frac{7}{7}$ .

$\frac{q \cdot 7}{5 \cdot 7} - \frac{2 q}{7} \cdot \frac{5}{5} + \frac{2}{5} = - \frac{11}{7}$

Step 1.4.2

Multiply $5$ by $7$ .

$\frac{q \cdot 7}{35} - \frac{2 q}{7} \cdot \frac{5}{5} + \frac{2}{5} = - \frac{11}{7}$

Step 1.4.3

Multiply $\frac{2 q}{7}$ by $\frac{5}{5}$ .

$\frac{q \cdot 7}{35} - \frac{2 q \cdot 5}{7 \cdot 5} + \frac{2}{5} = - \frac{11}{7}$

Step 1.4.4

Multiply $7$ by $5$ .

$\frac{q \cdot 7}{35} - \frac{2 q \cdot 5}{35} + \frac{2}{5} = - \frac{11}{7}$

Step 1.5

Combine the numerators over the common denominator.

$\frac{q \cdot 7 - 2 q \cdot 5}{35} + \frac{2}{5} = - \frac{11}{7}$

Step 1.6

Simplify each term.

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Step 1.6.1

Simplify the numerator.

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Step 1.6.1.1

Factor $q$ out of $q \cdot 7 - 2 q \cdot 5$ .

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Step 1.6.1.1.1

Factor $q$ out of $q \cdot 7$ .

$\frac{q (7) - 2 q \cdot 5}{35} + \frac{2}{5} = - \frac{11}{7}$

Step 1.6.1.1.2

Factor $q$ out of $- 2 q \cdot 5$ .

$\frac{q (7) + q (- 2 \cdot 5)}{35} + \frac{2}{5} = - \frac{11}{7}$

Step 1.6.1.1.3

Factor $q$ out of $q (7) + q (- 2 \cdot 5)$ .

$\frac{q (7 - 2 \cdot 5)}{35} + \frac{2}{5} = - \frac{11}{7}$

Step 1.6.1.2

Multiply $- 2$ by $5$ .

$\frac{q (7 - 10)}{35} + \frac{2}{5} = - \frac{11}{7}$

Step 1.6.1.3

Subtract $10$ from $7$ .

$\frac{q \cdot - 3}{35} + \frac{2}{5} = - \frac{11}{7}$

Step 1.6.2

Move $- 3$ to the left of $q$ .

$\frac{- 3 \cdot q}{35} + \frac{2}{5} = - \frac{11}{7}$

Step 1.6.3

Move the negative in front of the fraction.

$- \frac{3 q}{35} + \frac{2}{5} = - \frac{11}{7}$

Step 2

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

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Step 2.1

Subtract $\frac{2}{5}$ from both sides of the equation.

$- \frac{3 q}{35} = - \frac{11}{7} - \frac{2}{5}$

Step 2.2

To write $- \frac{11}{7}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$- \frac{3 q}{35} = - \frac{11}{7} \cdot \frac{5}{5} - \frac{2}{5}$

Step 2.3

To write $- \frac{2}{5}$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$- \frac{3 q}{35} = - \frac{11}{7} \cdot \frac{5}{5} - \frac{2}{5} \cdot \frac{7}{7}$

Step 2.4

Write each expression with a common denominator of $35$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.4.1

Multiply $\frac{11}{7}$ by $\frac{5}{5}$ .

$- \frac{3 q}{35} = - \frac{11 \cdot 5}{7 \cdot 5} - \frac{2}{5} \cdot \frac{7}{7}$

Step 2.4.2

Multiply $7$ by $5$ .

$- \frac{3 q}{35} = - \frac{11 \cdot 5}{35} - \frac{2}{5} \cdot \frac{7}{7}$

Step 2.4.3

Multiply $\frac{2}{5}$ by $\frac{7}{7}$ .

$- \frac{3 q}{35} = - \frac{11 \cdot 5}{35} - \frac{2 \cdot 7}{5 \cdot 7}$

Step 2.4.4

Multiply $5$ by $7$ .

$- \frac{3 q}{35} = - \frac{11 \cdot 5}{35} - \frac{2 \cdot 7}{35}$

Step 2.5

Combine the numerators over the common denominator.

$- \frac{3 q}{35} = \frac{- 11 \cdot 5 - 2 \cdot 7}{35}$

Step 2.6

Simplify the numerator.

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Step 2.6.1

Multiply $- 11$ by $5$ .

$- \frac{3 q}{35} = \frac{- 55 - 2 \cdot 7}{35}$

Step 2.6.2

Multiply $- 2$ by $7$ .

$- \frac{3 q}{35} = \frac{- 55 - 14}{35}$

Step 2.6.3

Subtract $14$ from $- 55$ .

$- \frac{3 q}{35} = \frac{- 69}{35}$

Step 2.7

Move the negative in front of the fraction.

$- \frac{3 q}{35} = - \frac{69}{35}$

Step 3

Since the expression on each side of the equation has the same denominator, the numerators must be equal.

$- 3 q = - 69$

Step 4

Divide each term in $- 3 q = - 69$ by $- 3$ and simplify.

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Step 4.1

Divide each term in $- 3 q = - 69$ by $- 3$ .

$\frac{- 3 q}{- 3} = \frac{- 69}{- 3}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $- 3$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{- 3 q}{- 3} = \frac{- 69}{- 3}$

Step 4.2.1.2

Divide $q$ by $1$ .

$q = \frac{- 69}{- 3}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Divide $- 69$ by $- 3$ .

$q = 23$