What is the answer to |x^3+x^2+x+1|=|x^3+1|+|x^2+x| ?

The answer to |x^3+x^2+x+1|=|x^3+1|+|x^2+x| is x=-1\lor x>= 0

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|x^3+x^2+x+1|=|x^3+1|+|x^2+x|

x^{3} + x^{2} + x + 1 = x^{3} + 1 + x^{2} + x

x = - 1 or x \geq 0

Solution steps

x^{3} + x^{2} + x + 1 = x^{3} + 1 + x^{2} + x

Find positive and negative intervals

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

Solve the inequality for each interval

x = - 1 or No Solution or x \geq 0

Merge Overlapping Intervals

x = - 1 or x \geq 0

∣ 2 x - 3 ∣ = ∣ 3 x + 5 ∣

2 ∣ x + 1 ∣^{2} - ∣ x + 1 ∣ = 3

∣ x + 2 ∣ + ∣ x - 3 ∣ + 2 = 0

∣ x - 3 ∣ + 2 ∣ x + 1 ∣ = 4

2 \cdot (∣ x + 1 ∣^{2}) - ∣ x + 1 ∣ = 3

What is the answer to |x^3+x^2+x+1|=|x^3+1|+|x^2+x| ?
The answer to |x^3+x^2+x+1|=|x^3+1|+|x^2+x| is x=-1\lor x>= 0
Solve for x: |x^3+x^2+x+1|=|x^3+1|+|x^2+x|
The solution is x=-1\lor x>= 0