Solve for k 5t=13-(9k)/7

$5 t = 13 - \frac{9 k}{7}$

Step 1

Rewrite the equation as $13 - \frac{9 k}{7} = 5 t$ .

$13 - \frac{9 k}{7} = 5 t$

Step 2

Subtract $13$ from both sides of the equation.

$- \frac{9 k}{7} = 5 t - 13$

Step 3

Multiply both sides of the equation by $- \frac{7}{9}$ .

$- \frac{7}{9} (- \frac{9 k}{7}) = - \frac{7}{9} (5 t - 13)$

Step 4

Simplify both sides of the equation.

Simplify the left side.

Simplify $- \frac{7}{9} (- \frac{9 k}{7})$ .

Cancel the common factor of $7$ .

Move the leading negative in $- \frac{7}{9}$ into the numerator.

$\frac{- 7}{9} (- \frac{9 k}{7}) = - \frac{7}{9} (5 t - 13)$

Move the leading negative in $- \frac{9 k}{7}$ into the numerator.

$\frac{- 7}{9} \cdot \frac{- 9 k}{7} = - \frac{7}{9} (5 t - 13)$

Factor $7$ out of $- 7$ .

$\frac{7 (- 1)}{9} \cdot \frac{- 9 k}{7} = - \frac{7}{9} (5 t - 13)$

Cancel the common factor.

$\frac{7 \cdot - 1}{9} \cdot \frac{- 9 k}{7} = - \frac{7}{9} (5 t - 13)$

Rewrite the expression.

$\frac{- 1}{9} (- 9 k) = - \frac{7}{9} (5 t - 13)$

Cancel the common factor of $9$ .

Factor $9$ out of $- 9 k$ .

$\frac{- 1}{9} (9 (- k)) = - \frac{7}{9} (5 t - 13)$

Cancel the common factor.

$\frac{- 1}{9} (9 (- k)) = - \frac{7}{9} (5 t - 13)$

Rewrite the expression.

$- - k = - \frac{7}{9} (5 t - 13)$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 k = - \frac{7}{9} (5 t - 13)$

Multiply $k$ by $1$ .

$k = - \frac{7}{9} (5 t - 13)$

Simplify the right side.

Simplify $- \frac{7}{9} (5 t - 13)$ .

Apply the distributive property.

$k = - \frac{7}{9} (5 t) - \frac{7}{9} \cdot - 13$

Multiply $- \frac{7}{9} (5 t)$ .

Multiply $5$ by $- 1$ .

$k = - 5 (\frac{7}{9}) t - \frac{7}{9} \cdot - 13$

Combine $- 5$ and $\frac{7}{9}$ .

$k = \frac{- 5 \cdot 7}{9} t - \frac{7}{9} \cdot - 13$

Multiply $- 5$ by $7$ .

$k = \frac{- 35}{9} t - \frac{7}{9} \cdot - 13$

Combine $\frac{- 35}{9}$ and $t$ .

$k = \frac{- 35 t}{9} - \frac{7}{9} \cdot - 13$

Multiply $- \frac{7}{9} \cdot - 13$ .

Multiply $- 13$ by $- 1$ .

$k = \frac{- 35 t}{9} + 13 (\frac{7}{9})$

Combine $13$ and $\frac{7}{9}$ .

$k = \frac{- 35 t}{9} + \frac{13 \cdot 7}{9}$

Multiply $13$ by $7$ .

$k = \frac{- 35 t}{9} + \frac{91}{9}$

Move the negative in front of the fraction.

$k = - \frac{35 t}{9} + \frac{91}{9}$

Solve for k 5t=13-(9k)/7

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