SOLUTION: Hi Sir/ Mdm., I come to a question of inequalities which made me feel curious, the question and working is as below: x-1/(x+1)≥ 2 X � 1 ≥ 2( x +1) x-1 ≥ 2

Question 496612: Hi Sir/ Mdm.,
I come to a question of inequalities which made me feel curious, the question and working is as below:
x-1/(x+1)≥ 2
X � 1 ≥ 2( x +1)
x-1 ≥ 2x +2
x -2x ≥2+1
-x ≥ 3
X ≤ -3
Since X ≤ -3, so the possible values for x will be -3,-4,-5,....
Am I right?
I test the inequalities with -3, the answer is 2≥ 2, so it is acceptable,
But why when I test the inequalities with - 4 and so on , the value is less than 2,
So does that mean this inequalities only have one possible value of x, that is x=-3.
So should I write my answer as X ≤ -3, or x= -3?
Answer by scott8148(6628) (Show Source): You can put this solution on YOUR website!
using hindsight from your 1st solution, x seems to be negative

this means that in the second line of the solution (where you multiplied by x+1), the direction of the inequality should have changed
___ this sometimes happens when the sign of a quantity is unknown
___ that's why you check at the end of a solution
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SOLUTION: Hi Sir/ Mdm., I come to a question of inequalities which made me feel curious, the question and working is as below: x-1/(x+1)&#8805; 2 X � 1 &#8805; 2( x +1) x-1 &#8805; 2

SOLUTION: Hi Sir/ Mdm., I come to a question of inequalities which made me feel curious, the question and working is as below: x-1/(x+1)≥ 2 X � 1 ≥ 2( x +1) x-1 ≥ 2