A student is attempting to solve the equation

Here is their working:

The first solution is given by

$$\frac{x}{2}+3=x\Rightarrow x=6$$

and the second is given by

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

so the solutions are

$$x=6,x=-2$$

1. Prove, by substituting the solutions back into the original equation, that the student is wrong.

2. Explain, by drawing a diagram, why the student's working is incorrect.