Solve operatorname{si}3(x+2)-2(x+1)=8

$$\operatorname { si } 3 ( x + 2 ) - 2 ( x + 1 ) = 8$$

Solve for s

$$s=\frac{2\left(x+5\right)}{3\left(ix+2i\right)}$$

$$x\neq -2$$

Steps for Solving Linear Equation

Use the distributive property to multiply s\times \left(3i\right) by x+2.

$$3isx+2s\times \left(3i\right)-2\left(x+1\right)=8$$

Multiply 2 and 3i to get 6i.

$$3isx+6is-2\left(x+1\right)=8$$

Use the distributive property to multiply -2 by x+1.

$$3isx+6is-2x-2=8$$

Add 2x to both sides.

$$3isx+6is-2=8+2x$$

Add 2 to both sides.

$$3isx+6is=8+2x+2$$

Add 8 and 2 to get 10.

$$3isx+6is=10+2x$$

Combine all terms containing s.

$$\left(3ix+6i\right)s=10+2x$$

The equation is in standard form.

$$\left(3ix+6i\right)s=2x+10$$

Divide both sides by 6i+3ix.

$$\frac{\left(3ix+6i\right)s}{3ix+6i}=\frac{2x+10}{3ix+6i}$$

Dividing by 6i+3ix undoes the multiplication by 6i+3ix.

$$s=\frac{2x+10}{3ix+6i}$$

Divide 10+2x by 6i+3ix.

$$s=\frac{2\left(x+5\right)}{3\left(ix+2i\right)}$$

Solve for x

$$x=-\frac{2\left(3is-5\right)}{3is-2}$$

$$s\neq -\frac{2}{3}i$$

Steps for Solving Linear Equation

Use the distributive property to multiply s\times \left(3i\right) by x+2.

$$3isx+2s\times \left(3i\right)-2\left(x+1\right)=8$$

Multiply 2 and 3i to get 6i.

$$3isx+6is-2\left(x+1\right)=8$$

Use the distributive property to multiply -2 by x+1.

$$3isx+6is-2x-2=8$$

Subtract 6is from both sides.

$$3isx-2x-2=8-6is$$

Add 2 to both sides.

$$3isx-2x=8-6is+2$$

Add 8 and 2 to get 10.

$$3isx-2x=10-6is$$

Combine all terms containing x.

$$\left(3is-2\right)x=10-6is$$

Divide both sides by 3is-2.

$$\frac{\left(3is-2\right)x}{3is-2}=\frac{10-6is}{3is-2}$$

Dividing by 3is-2 undoes the multiplication by 3is-2.

$$x=\frac{10-6is}{3is-2}$$

Divide 10-6is by 3is-2.

$$x=\frac{2\left(5-3is\right)}{3is-2}$$