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-x+6+x\geq 1
Add x to both sides.
-x+x\geq 1-6
Subtract 6 from both sides.
-x+x\geq -5
Subtract 6 from 1 to get -5.
0\geq -5
Combine -x and x to get 0.
x\in \mathrm{R}
This is true for any x.