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-\frac{1}{3}x+1-\frac{2}{3}x\leq 0
Subtract \frac{2}{3}x from both sides.
-x+1\leq 0
Combine -\frac{1}{3}x and -\frac{2}{3}x to get -x.
-x\leq -1
Subtract 1 from both sides. Anything subtracted from zero gives its negation.
x\geq \frac{-1}{-1}
Divide both sides by -1. Since -1 is negative, the inequality direction is changed.
x\geq 1
Divide -1 by -1 to get 1.