What is |x-1|-|x-2|+|x-3|>= 6 ?

The solution to |x-1|-|x-2|+|x-3|>= 6 is x = 8

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|x-1|-|x-2|+|x-3|>= 6

∣ x - 1 ∣ - ∣ x - 2 ∣ + ∣ x - 3 ∣ \geq 6

x \leq - 4 or x \geq 8

Solution steps

∣ x - 1 ∣ - ∣ x - 2 ∣ + ∣ x - 3 ∣ \geq 6

Find positive and negative intervals

x < 1, 1 \leq x < 2, 2 \leq x < 3, x \geq 3

Solve the inequality for each interval

x \leq - 4 or No Solution or x \geq 8

Merge Overlapping Intervals

x \leq - 4 or x \geq 8

x^{2} - x \leq x + 1

∣ 2 x - 3 ∣ > ∣ x + 4 ∣

∣ - 0.5 x ∣ < 1

[\frac{( x ^{2} - 5 x + 6 )}{( ∣ x ∣ + 7 )}] < 0

∣ 4 - 3 x ∣ - 2 > 0

What is |x-1|-|x-2|+|x-3|>= 6 ?
The solution to |x-1|-|x-2|+|x-3|>= 6 is x<=-4\lor x>= 8