Solve for q k=-q/p+1

$k = - \frac{q}{p} + 1$

Step 1

Rewrite the equation as $- \frac{q}{p} + 1 = k$ .

$- \frac{q}{p} + 1 = k$

Step 2

Subtract $1$ from both sides of the equation.

$- \frac{q}{p} = k - 1$

Step 3

Divide each term in $- \frac{q}{p} = k - 1$ by $- 1$ and simplify.

Divide each term in $- \frac{q}{p} = k - 1$ by $- 1$ .

$\frac{- \frac{q}{p}}{- 1} = \frac{k}{- 1} + \frac{- 1}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{\frac{q}{p}}{1} = \frac{k}{- 1} + \frac{- 1}{- 1}$

Divide $\frac{q}{p}$ by $1$ .

$\frac{q}{p} = \frac{k}{- 1} + \frac{- 1}{- 1}$

Simplify the right side.

Simplify each term.

Move the negative one from the denominator of $\frac{k}{- 1}$ .

$\frac{q}{p} = - 1 \cdot k + \frac{- 1}{- 1}$

Rewrite $- 1 \cdot k$ as $- k$ .

$\frac{q}{p} = - k + \frac{- 1}{- 1}$

Divide $- 1$ by $- 1$ .

$\frac{q}{p} = - k + 1$

Step 4

Multiply both sides by $p$ .

$\frac{q}{p} p = (- k + 1) p$

Step 5

Simplify.

Simplify the left side.

Cancel the common factor of $p$ .

Cancel the common factor.

$\frac{q}{p} p = (- k + 1) p$

Rewrite the expression.

$q = (- k + 1) p$

Simplify the right side.

Simplify $(- k + 1) p$ .

Apply the distributive property.

$q = - k p + 1 p$

Multiply $p$ by $1$ .

$q = - k p + p$