What is |x-1|+|x-2|+2|x-3|<0 ?

The solution to |x-1|+|x-2|+2|x-3|<0 is No Solution for x\in\mathbb{R}

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|x-1|+|x-2|+2|x-3|<0

∣ x - 1 ∣ + ∣ x - 2 ∣ + 2 ∣ x - 3 ∣ < 0

No Solution for x \in R

Solution steps

∣ x - 1 ∣ + ∣ x - 2 ∣ + 2 ∣ x - 3 ∣ < 0

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 for x \in R

\frac{( x - 1 )}{( x - 2 )} \leq 3

\frac{( 3 - 4 x )}{5} \leq 4

34 + 21 x - x^{2} \leq - 1

∣ x + 2 ∣ + ∣ x ∣ + ∣ x - 2 ∣ > 6

\frac{( x - 3 )}{( x + 1 )} \leq 2

What is |x-1|+|x-2|+2|x-3|<0 ?
The solution to |x-1|+|x-2|+2|x-3|<0 is No Solution for x\in\mathbb{R}