Solve for q 2/7=4/5+9q

$\frac{2}{7} = \frac{4}{5} + 9 q$

Step 1

Rewrite the equation as $\frac{4}{5} + 9 q = \frac{2}{7}$ .

$\frac{4}{5} + 9 q = \frac{2}{7}$

Step 2

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

Subtract $\frac{4}{5}$ from both sides of the equation.

$9 q = \frac{2}{7} - \frac{4}{5}$

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

$9 q = \frac{2}{7} \cdot \frac{5}{5} - \frac{4}{5}$

To write $- \frac{4}{5}$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$9 q = \frac{2}{7} \cdot \frac{5}{5} - \frac{4}{5} \cdot \frac{7}{7}$

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

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

$9 q = \frac{2 \cdot 5}{7 \cdot 5} - \frac{4}{5} \cdot \frac{7}{7}$

Multiply $7$ by $5$ .

$9 q = \frac{2 \cdot 5}{35} - \frac{4}{5} \cdot \frac{7}{7}$

Multiply $\frac{4}{5}$ by $\frac{7}{7}$ .

$9 q = \frac{2 \cdot 5}{35} - \frac{4 \cdot 7}{5 \cdot 7}$

Multiply $5$ by $7$ .

$9 q = \frac{2 \cdot 5}{35} - \frac{4 \cdot 7}{35}$

Combine the numerators over the common denominator.

$9 q = \frac{2 \cdot 5 - 4 \cdot 7}{35}$

Simplify the numerator.

Multiply $2$ by $5$ .

$9 q = \frac{10 - 4 \cdot 7}{35}$

Multiply $- 4$ by $7$ .

$9 q = \frac{10 - 28}{35}$

Subtract $28$ from $10$ .

$9 q = \frac{- 18}{35}$

Move the negative in front of the fraction.

$9 q = - \frac{18}{35}$

Step 3

Divide each term in $9 q = - \frac{18}{35}$ by $9$ and simplify.

Divide each term in $9 q = - \frac{18}{35}$ by $9$ .

$\frac{9 q}{9} = \frac{- \frac{18}{35}}{9}$

Simplify the left side.

Cancel the common factor of $9$ .

Cancel the common factor.

$\frac{9 q}{9} = \frac{- \frac{18}{35}}{9}$

Divide $q$ by $1$ .

$q = \frac{- \frac{18}{35}}{9}$

Simplify the right side.

Multiply the numerator by the reciprocal of the denominator.

$q = - \frac{18}{35} \cdot \frac{1}{9}$

Cancel the common factor of $9$ .

Move the leading negative in $- \frac{18}{35}$ into the numerator.

$q = \frac{- 18}{35} \cdot \frac{1}{9}$

Factor $9$ out of $- 18$ .

$q = \frac{9 (- 2)}{35} \cdot \frac{1}{9}$

Cancel the common factor.

$q = \frac{9 \cdot - 2}{35} \cdot \frac{1}{9}$

Rewrite the expression.

$q = \frac{- 2}{35}$

Move the negative in front of the fraction.

$q = - \frac{2}{35}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$q = - \frac{2}{35}$

Decimal Form:

$q = - 0.0\overline{571428}$

Solve for q 2/7=4/5+9q

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