Solve ax+1=2x

$$a x + 1 = 2 x$$

Solve for a

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

$$x\neq 0$$

Steps for Solving Linear Equation

Subtract 1 from both sides.

$$ax=2x-1$$

The equation is in standard form.

$$xa=2x-1$$

Divide both sides by x.

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

Dividing by x undoes the multiplication by x.

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

Divide 2x-1 by x.

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

Solve for x

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

$$a\neq 2$$

Steps for Solving Linear Equation

Subtract 2x from both sides.

$$ax+1-2x=0$$

Subtract 1 from both sides. Anything subtracted from zero gives its negation.

$$ax-2x=-1$$

Combine all terms containing x.

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

Divide both sides by a-2.

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

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

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