Solve (2+a=left(1+aright)x

$$(2+a = \left( 1+a \right) x$$

Solve for a

$$a=-\frac{2-x}{1-x}$$

$$x\neq 1$$

Steps for Solving Linear Equation

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

$$2+a=x+ax$$

Subtract ax from both sides.

$$2+a-ax=x$$

Subtract 2 from both sides.

$$a-ax=x-2$$

Combine all terms containing a.

$$\left(1-x\right)a=x-2$$

Divide both sides by -x+1.

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

Dividing by -x+1 undoes the multiplication by -x+1.

$$a=\frac{x-2}{1-x}$$

Solve for x

$$x=\frac{a+2}{a+1}$$

$$a\neq -1$$

Steps for Solving Linear Equation

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

$$2+a=x+ax$$

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

$$x+ax=2+a$$

Combine all terms containing x.

$$\left(1+a\right)x=2+a$$

The equation is in standard form.

$$\left(a+1\right)x=a+2$$

Divide both sides by 1+a.

$$\frac{\left(a+1\right)x}{a+1}=\frac{a+2}{a+1}$$

Dividing by 1+a undoes the multiplication by 1+a.

$$x=\frac{a+2}{a+1}$$