Solve -2a+10=ax+b

$$- 2 a + 10 = a x + b$$

Solve for a (complex solution)

$$\left\{\begin{matrix}a=\frac{10-b}{x+2}\text{, }&x\neq -2\\a\in \mathrm{C}\text{, }&b=10\text{ and }x=-2\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract ax from both sides.

$$-2a+10-ax=b$$

Subtract 10 from both sides.

$$-2a-ax=b-10$$

Combine all terms containing a.

$$\left(-2-x\right)a=b-10$$

The equation is in standard form.

$$\left(-x-2\right)a=b-10$$

Divide both sides by -x-2.

$$\frac{\left(-x-2\right)a}{-x-2}=\frac{b-10}{-x-2}$$

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

$$a=\frac{b-10}{-x-2}$$

Divide b-10 by -x-2.

$$a=-\frac{b-10}{x+2}$$

Solve for a

$$\left\{\begin{matrix}a=\frac{10-b}{x+2}\text{, }&x\neq -2\\a\in \mathrm{R}\text{, }&b=10\text{ and }x=-2\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract ax from both sides.

$$-2a+10-ax=b$$

Subtract 10 from both sides.

$$-2a-ax=b-10$$

Combine all terms containing a.

$$\left(-2-x\right)a=b-10$$

The equation is in standard form.

$$\left(-x-2\right)a=b-10$$

Divide both sides by -x-2.

$$\frac{\left(-x-2\right)a}{-x-2}=\frac{b-10}{-x-2}$$

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

$$a=\frac{b-10}{-x-2}$$

Divide b-10 by -x-2.

$$a=-\frac{b-10}{x+2}$$

Solve for b

$$b=10-2a-ax$$

Solution Steps

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

$$ax+b=-2a+10$$

Subtract ax from both sides.

$$b=-2a+10-ax$$