Answer
$E_x = -1000~V/m$
Work Step by Step
We can find $E_x$:
$E_x = -\frac{\Delta V}{\Delta x}$
$E_x = -\frac{1000~ V-(-1000~V)}{1.0~m-(-1.0~m)}$
$E_x = -1000~V/m$
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