Question

|x|>|x+1|
Va rog mult

Answer 1

|x| > |x+1|
|x| - |x+1| > 0

S1: x-(x+1)> 0, x ≥ 0, x+1 ≥ 0
S2: -x-(x+1) > 0, x<0, x+1 ≥ 0
S3:  x-(-(x+1)) > 0, x ≥0, x+1 < 0
S4: -x -(-(x+1)) > 0, x<0 , x+1<0

S1: x ∈ ∅, x ≥ 0, x ≥ -1
S2: x< - $\frac{1}{2}$ , x < 0, x ≥  -1
S3: x> $- \frac{1}{2}$ , x ≥0 , x < -1
S4: x ∈ R, x < 0, x < -1

S1: x ∈∅, x ∈ [0, +∞)
S2: x< $-\frac{1}{2}$ , x ∈ [ -1; 0)
S3: x> $-\frac{1}{2}$ , x ∈ ∅
S4: x ∈ R, x ∈ ( -∞, -1)

S1: x ∈ ∅
S2: x ∈ $[ -1, - \frac{1}{2} )$
S3: x ∈ ∅
S4: x ∈ ( -∞ , -1)

Din S2 si S4⇒ x ∈ ( -∞ , $-\frac{1}{2}$ )