Solve -q+k/-(1+k)=-1

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

Solve for k

$$k=\frac{-q-1}{2}$$

$$q\neq 1$$

Steps for Solving Linear Equation

To find the opposite of 1+k, find the opposite of each term.

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

Variable k cannot be equal to -1 since division by zero is not defined. Multiply both sides of the equation by -k-1.

$$-\left(q+k\right)=-\left(-k-1\right)$$

Cancel out -1 on both sides.

$$q+k=-k-1$$

Add k to both sides.

$$q+k+k=-1$$

Combine k and k to get 2k.

$$q+2k=-1$$

Subtract q from both sides.

$$2k=-1-q$$

The equation is in standard form.

$$2k=-q-1$$

Divide both sides by 2.

$$\frac{2k}{2}=\frac{-q-1}{2}$$

Dividing by 2 undoes the multiplication by 2.

$$k=\frac{-q-1}{2}$$

Variable k cannot be equal to -1.

$$k=\frac{-q-1}{2}\text{, }k\neq -1$$

Solve for q

$$q=-2k-1$$

$$k\neq -1$$

Solution Steps

To find the opposite of 1+k, find the opposite of each term.

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

Multiply both sides of the equation by -k-1.

$$-\left(q+k\right)=-\left(-k-1\right)$$

Cancel out -1 on both sides.

$$q+k=-k-1$$

Subtract k from both sides.

$$q=-k-1-k$$

Combine -k and -k to get -2k.

$$q=-2k-1$$