What is |x-11|+|x+2|<= 1/4 ?

The solution to |x-11|+|x+2|<= 1/4 is No Solution for x\in\mathbb{R}

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|x-11|+|x+2|<= 1/4

∣ x - 11 ∣ + ∣ x + 2 ∣ \leq \frac{1}{4}

No Solution for x \in R

Solution steps

∣ x - 11 ∣ + ∣ x + 2 ∣ \leq \frac{1}{4}

Find positive and negative intervals

x < - 2, - 2 \leq x < 11, x \geq 11

Solve the inequality for each interval

No Solution for x \in R

x^{2} - 4 > x^{2} - 4

x^{2} - 5 ∣ x ∣ + 6 \geq 0

x^{2} - 4 ∣ x ∣ + 3 < 0

∣ 4 (x - 1) + 10 ∣ \leq 22

∣ 3 x - 2 ∣ \geq ∣ x + 1 ∣

What is |x-11|+|x+2|<= 1/4 ?
The solution to |x-11|+|x+2|<= 1/4 is No Solution for x\in\mathbb{R}