Solve 3(x+a)-b=2(x+b)+a

$$3 ( x + a ) - b = 2 ( x + b ) + a$$

Solve for a

$$a=\frac{3b-x}{2}$$

Steps for Solving Linear Equation

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

$$3x+3a-b=2\left(x+b\right)+a$$

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

$$3x+3a-b=2x+2b+a$$

Subtract a from both sides.

$$3x+3a-b-a=2x+2b$$

Combine 3a and -a to get 2a.

$$3x+2a-b=2x+2b$$

Subtract 3x from both sides.

$$2a-b=2x+2b-3x$$

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

$$2a-b=-x+2b$$

Add b to both sides.

$$2a=-x+2b+b$$

Combine 2b and b to get 3b.

$$2a=-x+3b$$

The equation is in standard form.

$$2a=3b-x$$

Divide both sides by 2.

$$\frac{2a}{2}=\frac{3b-x}{2}$$

Dividing by 2 undoes the multiplication by 2.

$$a=\frac{3b-x}{2}$$

Solve for b

$$b=\frac{x+2a}{3}$$

Steps for Solving Linear Equation

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

$$3x+3a-b=2\left(x+b\right)+a$$

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

$$3x+3a-b=2x+2b+a$$

Subtract 2b from both sides.

$$3x+3a-b-2b=2x+a$$

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

$$3x+3a-3b=2x+a$$

Subtract 3x from both sides.

$$3a-3b=2x+a-3x$$

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

$$3a-3b=-x+a$$

Subtract 3a from both sides.

$$-3b=-x+a-3a$$

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

$$-3b=-x-2a$$

Divide both sides by -3.

$$\frac{-3b}{-3}=\frac{-x-2a}{-3}$$

Dividing by -3 undoes the multiplication by -3.

$$b=\frac{-x-2a}{-3}$$

Divide -x-2a by -3.

$$b=\frac{x+2a}{3}$$