If you notice, the (x+1) term is being squared, then being square rooted. Since these are operations that undo each other, they will cancel out. Don't forget, what you do to one side you do to the other. But 1^2 = 1 and sqrt(1) = 1 so in this case it is not worth worrying about.
So now you have x+1 <= 1, which means that x <= 0.
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(x + 1 )^2 <= 1^2
(x + 1 )^2 <= 1
x^2 + 2x + 1 < = 1
x^2 + 2x <= 0
x(x + 2 ) <= 0
now to test the components.
I get - 2 <= x <= 0
If you notice, the (x+1) term is being squared, then being square rooted. Since these are operations that undo each other, they will cancel out. Don't forget, what you do to one side you do to the other. But 1^2 = 1 and sqrt(1) = 1 so in this case it is not worth worrying about.
So now you have x+1 <= 1, which means that x <= 0.
The other part is similar.