What is 2|x-1|+|2x-5|-2|x+2|<-8 ?

The solution to 2|x-1|+|2x-5|-2|x+2|<-8 is No Solution for x\in\mathbb{R}

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2|x-1|+|2x-5|-2|x+2|<-8

2 ∣ x - 1 ∣ + ∣ 2 x - 5 ∣ - 2 ∣ x + 2 ∣ < - 8

No Solution for x \in R

Solution steps

2 ∣ x - 1 ∣ + ∣ 2 x - 5 ∣ - 2 ∣ x + 2 ∣ < - 8

Find positive and negative intervals

x < - 2, - 2 \leq x < 1, 1 \leq x < \frac{5}{2}, x \geq \frac{5}{2}

Solve the inequality for each interval

No Solution for x \in R

x^{2} - ∣ 3 x - 2 ∣ > 0

∣ 9 - x ∣ < 2 - 3 x

∣ x - 1 ∣ + ∣ x - 2 ∣ > 3

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

∣ x - 2 ∣ > 2 + x - ∣ 3 - x ∣

What is 2|x-1|+|2x-5|-2|x+2|<-8 ?
The solution to 2|x-1|+|2x-5|-2|x+2|<-8 is No Solution for x\in\mathbb{R}