What is |x-1||x-2|>= |x+2| ?

The solution to |x-1||x-2|>= |x+2| is x = 4

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|x-1||x-2|>= |x+2|

∣ x - 1 ∣ ∣ x - 2 ∣ \geq ∣ x + 2 ∣

x \leq 0 or x \geq 4

Interval Notation

(- \infty, 0] \cup [4, \infty)

Solution steps

∣ x - 1 ∣ ∣ x - 2 ∣ \geq ∣ x + 2 ∣

Find positive and negative intervals

x < - 2, - 2 \leq x < 1, 1 \leq x < 2, x \geq 2

Solve the inequality for each interval

x < - 2 or - 2 \leq x \leq 0 or No Solution or x \geq 4

Merge Overlapping Intervals

x \leq 0 or x \geq 4

∣ 7 y ∣ - 2 > 5

x^{2} + 5 x < 6, ∣ x + 1 ∣ < 2

∣ x - 1 ∣ > - 1

∣ 2 - 4 x ∣ \leq 4

x^{2} - 4 x + 2 \geq ∣ x + 1 ∣

What is |x-1||x-2|>= |x+2| ?
The solution to |x-1||x-2|>= |x+2| is x<= 0\lor x>= 4