Solve 2ax+3=x+2a

$$2 a x + 3 = x + 2 a$$

Solve for a

$$a=-\frac{3-x}{2\left(x-1\right)}$$

$$x\neq 1$$

Steps for Solving Linear Equation

Subtract 2a from both sides.

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

Subtract 3 from both sides.

$$2ax-2a=x-3$$

Combine all terms containing a.

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

Divide both sides by 2x-2.

$$\frac{\left(2x-2\right)a}{2x-2}=\frac{x-3}{2x-2}$$

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

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

Divide x-3 by 2x-2.

$$a=\frac{x-3}{2\left(x-1\right)}$$

Solve for x

$$x=-\frac{3-2a}{2a-1}$$

$$a\neq \frac{1}{2}$$

Steps for Solving Linear Equation

Subtract x from both sides.

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

Subtract 3 from both sides.

$$2ax-x=2a-3$$

Combine all terms containing x.

$$\left(2a-1\right)x=2a-3$$

Divide both sides by 2a-1.

$$\frac{\left(2a-1\right)x}{2a-1}=\frac{2a-3}{2a-1}$$

Dividing by 2a-1 undoes the multiplication by 2a-1.

$$x=\frac{2a-3}{2a-1}$$