What is |x-1|+|2x-4|+|3x-9|<5 ?

The solution to |x-1|+|2x-4|+|3x-9|<5 is 7/4 <x< 19/6

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|x-1|+|2x-4|+|3x-9|<5

∣ x - 1 ∣ + ∣ 2 x - 4 ∣ + ∣ 3 x - 9 ∣ < 5

\frac{7}{4} < x < \frac{19}{6}

Solution steps

∣ x - 1 ∣ + ∣ 2 x - 4 ∣ + ∣ 3 x - 9 ∣ < 5

Find positive and negative intervals

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

Solve the inequality for each interval

No Solution or \frac{7}{4} < x < 2 or 2 \leq x < 3 or 3 \leq x < \frac{19}{6}

Merge Overlapping Intervals

\frac{7}{4} < x < \frac{19}{6}

∣ 2 x + 4 ∣ \geq ∣ x - 5 ∣

∣ x - 1 ∣ + ∣ x - 5 ∣ \leq 10

\frac{x ^{2} - 1}{x ^{2} + x + 1} < 1

∣ 2 (x - 1) + 4 ∣ < 4

∣ x - 1 ∣ + ∣ x - 3 ∣ \leq 6

What is |x-1|+|2x-4|+|3x-9|<5 ?
The solution to |x-1|+|2x-4|+|3x-9|<5 is 7/4 <x< 19/6