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

The solution to |x-1|+|x-2|+|x-3|<= 6 is 0<= x<= 4

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

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

0 \leq x \leq 4

Solution steps

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

0 \leq x < 1 or 1 \leq x < 2 or 2 \leq x < 3 or 3 \leq x \leq 4

Merge Overlapping Intervals

0 \leq x \leq 4

\frac{1}{∣ x - 2 ∣} \geq \frac{1}{4}

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

4 ∣ x - 2 ∣ - 2 - x < 4 x + 1

∣ x - 6 ∣ \geq 4

2 x - 7 x + 12 < ∣ x - 4 ∣

What is |x-1|+|x-2|+|x-3|<= 6 ?
The solution to |x-1|+|x-2|+|x-3|<= 6 is 0<= x<= 4