Lets say you have $y = -|3x - 1|$
when working out where it cuts the axis, particularly the x-coordinate you do the following
when $y = 0, 3x - 1 = 0$ therefore $x = 1/3 $
the modulus and the minus sign essentially is gone
but when you have $y = 2|x| - 1$ and you are trying to work out the x-coordinate
when $y = 0, 2|x| - 1 = 0$ therefore $|x| = -0.5$ hence no x value (but why?)
Why is it that the modulus sign essentially 'disappears' for the first function and not the second function written above? This is elementary, but I'm not thinking right. In the first case, is it essentially the same as -3x = 0, therefore dividing by -3 giving x = 0 (essentially doing the same above, dividing by -1 and the modulus - if that even makes sense?)
$$2|x|-1=0\iff |x|=\frac12\iff x=\pm\frac12$$
I can't understand why you wrote "hence no x value"...did you mean anything else? There are two real values that solve the above equality.