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

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

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

∣ x - 1 ∣ + ∣ x - 2 ∣ > 3

x < 0 or x > 3

Solution steps

∣ x - 1 ∣ + ∣ x - 2 ∣ > 3

Find positive and negative intervals

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

Solve the inequality for each interval

x < 0 or No Solution or x > 3

Merge Overlapping Intervals

x < 0 or x > 3

- x^{2} - 9 x - 7 \geq 1

∣ x - 2 ∣ > 2 + x - ∣ 3 - x ∣

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

\frac{1}{∣ x - 2 ∣} \geq \frac{1}{4}

\frac{5}{( 3 - x )} > 1