Solve 3[k(x+1)+b]-2[k(x-1))=2x+17

$$3 [ k ( x + 1 ) + b ] - 2 [ k ( x - 1 ) ) = 2 x + 17$$

Solve for k (complex solution)

$$\left\{\begin{matrix}k=-\frac{-2x+3b-17}{x+5}\text{, }&x\neq -5\\k\in \mathrm{C}\text{, }&x=-5\text{ and }b=\frac{7}{3}\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply k by x+1.

$$3\left(kx+k+b\right)-2k\left(x-1\right)=2x+17$$

Use the distributive property to multiply 3 by kx+k+b.

$$3kx+3k+3b-2k\left(x-1\right)=2x+17$$

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

$$3kx+3k+3b-2kx+2k=2x+17$$

Combine 3kx and -2kx to get kx.

$$kx+3k+3b+2k=2x+17$$

Combine 3k and 2k to get 5k.

$$kx+5k+3b=2x+17$$

Subtract 3b from both sides.

$$kx+5k=2x+17-3b$$

Combine all terms containing k.

$$\left(x+5\right)k=2x+17-3b$$

The equation is in standard form.

$$\left(x+5\right)k=2x-3b+17$$

Divide both sides by x+5.

$$\frac{\left(x+5\right)k}{x+5}=\frac{2x-3b+17}{x+5}$$

Dividing by x+5 undoes the multiplication by x+5.

$$k=\frac{2x-3b+17}{x+5}$$

Solve for b

$$b=\frac{17-5k+2x-kx}{3}$$

Steps for Solving Linear Equation

Use the distributive property to multiply k by x+1.

$$3\left(kx+k+b\right)-2k\left(x-1\right)=2x+17$$

Use the distributive property to multiply 3 by kx+k+b.

$$3kx+3k+3b-2k\left(x-1\right)=2x+17$$

Add 2k\left(x-1\right) to both sides.

$$3kx+3k+3b=2x+17+2k\left(x-1\right)$$

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

$$3kx+3k+3b=2x+17+2kx-2k$$

Subtract 3kx from both sides.

$$3k+3b=2x+17+2kx-2k-3kx$$

Combine 2kx and -3kx to get -kx.

$$3k+3b=2x+17-kx-2k$$

Subtract 3k from both sides.

$$3b=2x+17-kx-2k-3k$$

Combine -2k and -3k to get -5k.

$$3b=2x+17-kx-5k$$

The equation is in standard form.

$$3b=17-5k+2x-kx$$

Divide both sides by 3.

$$\frac{3b}{3}=\frac{17-5k+2x-kx}{3}$$

Dividing by 3 undoes the multiplication by 3.

$$b=\frac{17-5k+2x-kx}{3}$$

Solve for k

$$\left\{\begin{matrix}k=-\frac{-2x+3b-17}{x+5}\text{, }&x\neq -5\\k\in \mathrm{R}\text{, }&x=-5\text{ and }b=\frac{7}{3}\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply k by x+1.

$$3\left(kx+k+b\right)-2k\left(x-1\right)=2x+17$$

Use the distributive property to multiply 3 by kx+k+b.

$$3kx+3k+3b-2k\left(x-1\right)=2x+17$$

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

$$3kx+3k+3b-2kx+2k=2x+17$$

Combine 3kx and -2kx to get kx.

$$kx+3k+3b+2k=2x+17$$

Combine 3k and 2k to get 5k.

$$kx+5k+3b=2x+17$$

Subtract 3b from both sides.

$$kx+5k=2x+17-3b$$

Combine all terms containing k.

$$\left(x+5\right)k=2x+17-3b$$

The equation is in standard form.

$$\left(x+5\right)k=2x-3b+17$$

Divide both sides by x+5.

$$\frac{\left(x+5\right)k}{x+5}=\frac{2x-3b+17}{x+5}$$

Dividing by x+5 undoes the multiplication by x+5.

$$k=\frac{2x-3b+17}{x+5}$$