Solve (2y-2)=sin(1.5x+1)

$$( 2 y - 2 ) = \sin ( 1.5 x + 1 )$$

Solve for y

$$y=\frac{\sin(\frac{3x}{2}+1)+2}{2}$$

Steps for Solving Linear Equation

Add 2 to both sides.

$$2y=\sin(1.5x+1)+2$$

The equation is in standard form.

$$2y=\sin(\frac{3x}{2}+1)+2$$

Divide both sides by 2.

$$\frac{2y}{2}=\frac{\sin(\frac{3x}{2}+1)+2}{2}$$

Dividing by 2 undoes the multiplication by 2.

$$y=\frac{\sin(\frac{3x}{2}+1)+2}{2}$$

Divide \sin(\frac{3x}{2}+1)+2 by 2.

$$y=\frac{\sin(\frac{3x+2}{2})+2}{2}$$

Solve for x

$$x=\frac{2\left(-\arcsin(2\left(1-y\right))+2\pi n_{1}-1\right)}{3}\text{, }n_{1}\in \mathrm{Z}$$

$$x=\frac{2\left(\arcsin(2\left(1-y\right))+2\pi n_{2}+\pi -1\right)}{3}\text{, }n_{2}\in \mathrm{Z}\text{, }y\geq \frac{1}{2}\text{ and }y\leq \frac{3}{2}$$