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x-\left(-2\sqrt{2}\right)-\left(-1\right)>0
To find the opposite of -2\sqrt{2}-1, find the opposite of each term.
x+2\sqrt{2}-\left(-1\right)>0
The opposite of -2\sqrt{2} is 2\sqrt{2}.
x+2\sqrt{2}+1>0
The opposite of -1 is 1.
x+1>-2\sqrt{2}
Subtract 2\sqrt{2} from both sides. Anything subtracted from zero gives its negation.
x>-2\sqrt{2}-1
Subtract 1 from both sides.