Simplex algorithm : can't do it !

Hi,

I feel terribly dumb, but I just can't do this...

Objective function :
$\displaystyle$\indent z = min \; \; x_{1} + 2x_{2}$$Constraints : \displaystyle x_{1} - x_{2} \le -3$$
$\displaystyle$x_{1} + x_{2} \le 5$$\displaystyle x_{1} + x_{2} \ge 0$$

Constraints under the canonic form (I'm probably wrong here) :
$\displaystyle$-x_{1} + x_{2} - x_{3} = 3$$\displaystyle x_{1} + x_{2} + x_{4} = 5$$
$\displaystyle$-x_{1} - x_{2} + x_{5} = 0$$Let's rewrite using x3, x4, x5 as basic variables : \displaystyle \indent x_{3} = -x_{1} + x_{2} - 3$$
$\displaystyle$\indent x_{4} = -x_{1} - x_{2} + 5$$\displaystyle \indent x_{5} = x_{1} + x_{2}$$

x1 "goes basic", let's test non-negativity :
$\displaystyle$\indent x_{3} \ge 0 \Rightarrow -x_{1} - 3 \ge 0 \Rightarrow x_{1} + 3 \le 0 \Rightarrow x_{1} \le -3$$\displaystyle \indent x_{4} \ge 0 \Rightarrow -x_{1} + 5 \ge 0 \Rightarrow x_{1} - 5 \le 0 \Rightarrow x_{1} \le 5$$
$\displaystyle$\indent x_{5} \ge 0 \Rightarrow x_{1} \ge 0

Error ! x1 has to be <= -3 AND >= 0 !

What did I do wrong ?

I had my constraints checked with an instructor and he said they were right.

Please note, this problem with only work when minimizing. It won't when maximizing because it is unbounb on a certain side. I would like to join a picture, but right now, I can't.