Solve ksinx/2-2k+1=0n

$$k \sin \frac { x } { 2 } - 2 k + 1 = 0 n$$

Solve for k

$$k=-\frac{1}{\sin(\frac{x}{2})-2}$$

Steps for Solving Linear Equation

Anything times zero gives zero.

$$k\sin(\frac{x}{2})-2k+1=0$$

Subtract 1 from both sides. Anything subtracted from zero gives its negation.

$$k\sin(\frac{x}{2})-2k=-1$$

Combine all terms containing k.

$$\left(\sin(\frac{x}{2})-2\right)k=-1$$

Divide both sides by \sin(\frac{1}{2}x)-2.

$$\frac{\left(\sin(\frac{x}{2})-2\right)k}{\sin(\frac{x}{2})-2}=-\frac{1}{\sin(\frac{x}{2})-2}$$

Dividing by \sin(\frac{1}{2}x)-2 undoes the multiplication by \sin(\frac{1}{2}x)-2.

$$k=-\frac{1}{\sin(\frac{x}{2})-2}$$

Solve for n

$$n\in \mathrm{R}$$

$$k=-\frac{1}{\sin(\frac{x}{2})-2}$$