Solve B=4a+2ab+a-ab+3

$$B = 4 a + 2 a b + a - a b + 3$$

Solve for B

$$B=ab+5a+3$$

Solution Steps

Combine 4a and a to get 5a.

$$B=5a+2ab-ab+3$$

Combine 2ab and -ab to get ab.

$$B=5a+ab+3$$

Solve for a

$$\left\{\begin{matrix}a=-\frac{3-B}{b+5}\text{, }&b\neq -5\\a\in \mathrm{R}\text{, }&B=3\text{ and }b=-5\end{matrix}\right.$$

Steps for Solving Linear Equation

Combine 4a and a to get 5a.

$$B=5a+2ab-ab+3$$

Combine 2ab and -ab to get ab.

$$B=5a+ab+3$$

Swap sides so that all variable terms are on the left hand side.

$$5a+ab+3=B$$

Subtract 3 from both sides.

$$5a+ab=B-3$$

Combine all terms containing a.

$$\left(5+b\right)a=B-3$$

The equation is in standard form.

$$\left(b+5\right)a=B-3$$

Divide both sides by 5+b.

$$\frac{\left(b+5\right)a}{b+5}=\frac{B-3}{b+5}$$

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

$$a=\frac{B-3}{b+5}$$