Question about last inequality before equation (22) in Bell's EPR paper

In the penultimate inequality before equation (22) in Bell's EPR paper, we have

$|P(a,b)-P(a,c)|\leq 1+ P(b,c)+ \epsilon +\delta.~~~~~(1) $

Since $P(a,b)$ is equal to $-a\cdot b~ + (\epsilon + \delta)$ we could write (letting $\epsilon$ stand for the whole error)

$ |P(a,b)-P(a,c)|=|-a\cdot b+\epsilon_{ab}+a\cdot c -\epsilon_{bc}|.~~~~(2)$ At worst, the error in the r.h.s. above is 2x the larger of $(\epsilon_{ab},\epsilon_{ac})$. Suppose so. Now how do we know that the errors are not both positive, which would give:

$ |-a\cdot b+a\cdot c + 2(\epsilon +\delta)|\leq|a \cdot c-a\cdot b|+|2(\epsilon +\delta)|= |a \cdot c-a\cdot b|+ 2(\epsilon + \delta)?~~~~(3)$

To get equation (22) we need to have on the left hand side

$|a \cdot c-a\cdot b| -2(\epsilon + \delta). $

I am overlooking something sort of obvious I think, but the passage from (2) above to (3) does require caution, and I am trying to be cautious.

Thanks for any clarification.