What is (|x-1|+|x-2|)(|1-x|-|2-x|)>= x^2-6 ?

The solution to (|x-1|+|x-2|)(|1-x|-|2-x|)>= x^2-6 is -1<= x<= 3

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(|x-1|+|x-2|)(|1-x|-|2-x|)>= x^2-6

(∣ x - 1 ∣ + ∣ x - 2 ∣) (∣ 1 - x ∣ - ∣ 2 - x ∣) \geq x^{2} - 6

- 1 \leq x \leq 3

Interval Notation

[- 1, 3]

Solution steps

(∣ x - 1 ∣ + ∣ x - 2 ∣) (∣ 1 - x ∣ - ∣ 2 - x ∣) \geq x^{2} - 6

Find positive and negative intervals

x \leq 1, 1 < x \leq 2, x > 2

Solve the inequality for each interval

- 1 \leq x \leq 1 or 1 < x \leq 2 or 2 < x \leq 3

Merge Overlapping Intervals

- 1 \leq x \leq 3

\frac{5}{8} x^{2} - x - 12 = - x^{2} - 2 x + 234

3 y + 5 < 20

x^{2} - 2 x y - 3 y^{2}

\frac{1}{( 3 k ) ^{5}}

30 n^{2} b - 87 nb + 30 b

What is (|x-1|+|x-2|)(|1-x|-|2-x|)>= x^2-6 ?
The solution to (|x-1|+|x-2|)(|1-x|-|2-x|)>= x^2-6 is -1<= x<= 3