Solve b(x+2)+3(x+3)=4(x+1)

$$b ( x + 2 ) + 3 ( x + 3 ) = 4 ( x + 1 )$$

Solve for b

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

$$x\neq -2$$

Steps for Solving Linear Equation

Use the distributive property to multiply b by x+2.

$$bx+2b+3\left(x+3\right)=4\left(x+1\right)$$

Use the distributive property to multiply 3 by x+3.

$$bx+2b+3x+9=4\left(x+1\right)$$

Use the distributive property to multiply 4 by x+1.

$$bx+2b+3x+9=4x+4$$

Subtract 3x from both sides.

$$bx+2b+9=4x+4-3x$$

Combine 4x and -3x to get x.

$$bx+2b+9=x+4$$

Subtract 9 from both sides.

$$bx+2b=x+4-9$$

Subtract 9 from 4 to get -5.

$$bx+2b=x-5$$

Combine all terms containing b.

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

Divide both sides by x+2.

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

Dividing by x+2 undoes the multiplication by x+2.

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

Solve for x

$$x=-\frac{2b+5}{b-1}$$

$$b\neq 1$$

Steps for Solving Linear Equation

Use the distributive property to multiply b by x+2.

$$bx+2b+3\left(x+3\right)=4\left(x+1\right)$$

Use the distributive property to multiply 3 by x+3.

$$bx+2b+3x+9=4\left(x+1\right)$$

Use the distributive property to multiply 4 by x+1.

$$bx+2b+3x+9=4x+4$$

Subtract 4x from both sides.

$$bx+2b+3x+9-4x=4$$

Combine 3x and -4x to get -x.

$$bx+2b-x+9=4$$

Subtract 2b from both sides.

$$bx-x+9=4-2b$$

Subtract 9 from both sides.

$$bx-x=4-2b-9$$

Subtract 9 from 4 to get -5.

$$bx-x=-5-2b$$

Combine all terms containing x.

$$\left(b-1\right)x=-5-2b$$

The equation is in standard form.

$$\left(b-1\right)x=-2b-5$$

Divide both sides by b-1.

$$\frac{\left(b-1\right)x}{b-1}=\frac{-2b-5}{b-1}$$

Dividing by b-1 undoes the multiplication by b-1.

$$x=\frac{-2b-5}{b-1}$$

Divide -5-2b by b-1.

$$x=-\frac{2b+5}{b-1}$$