What is |x+1|>x+|x| ?

The solution to |x+1|>x+|x| is x<-1\lor-1<x<1

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|x+1|>x+|x|

∣ x + 1 ∣ > x + ∣ x ∣

x < - 1 or - 1 < x < 1

Solution steps

∣ x + 1 ∣ > x + ∣ x ∣

Find positive and negative intervals

x < - 1, - 1 \leq x < 0, x \geq 0

Solve the inequality for each interval

x < - 1 or - 1 < x < 0 or 0 \leq x < 1

Merge Overlapping Intervals

x < - 1 or - 1 < x < 1

7 x = 30

x^{- 2} \cdot x^{3}

\frac{x ^{2} + x - 56}{x ^{2} - 3 x - 28}

2 x - 3 (x - 1) = - 1

3 x^{3} - 2 x^{2} - 15 x + 10