What is |x^3-x+3|>= 3 ?

The solution to |x^3-x+3|>= 3 is x = 1

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|x^3-x+3|>= 3

x^{3} - x + 3 \geq 3

x \leq - 2 or - 1 \leq x \leq 0 or x \geq 1

Interval Notation

(- \infty, - 2] \cup [- 1, 0] \cup [1, \infty)

Solution steps

x^{3} - x + 3 \geq 3

Apply absolute rule: If

∣ u ∣ \geq a, a > 0

then

u \leq - a

u \geq a

x^{3} - x + 3 \leq - 3 or x^{3} - x + 3 \geq 3

x^{3} - x + 3 \leq - 3 or x^{3} - x + 3 \geq 3

x \leq - 2 or (- 1 \leq x \leq 0 or x \geq 1)

Merge Overlapping Intervals

x \leq - 2 or - 1 \leq x \leq 0 or x \geq 1

\frac{1}{4} + 2

- 25 m - 10 n

3 x^{2} = 44 x - 242

- 192

3 x^{2} - x + 9 = 0

What is |x^3-x+3|>= 3 ?
The solution to |x^3-x+3|>= 3 is x<=-2\lor-1<= x<= 0\lor x>= 1