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

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

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

∣ 1 - x ∣ + ∣ 3 x - 1 ∣ \leq 0

No Solution for x \in R

Solution steps

∣ 1 - x ∣ + ∣ 3 x - 1 ∣ \leq 0

Find positive and negative intervals

x < \frac{1}{3}, \frac{1}{3} \leq x \leq 1, x > 1

Solve the inequality for each interval

No Solution for x \in R

- 6 p + 18 > 6

x^{2} - 3

\frac{3}{4} (x - 1) = \frac{1}{4} (x + 2) + \frac{1}{2}

∣ x - 2 ∣ \geq 6

2 x + 3 > 4

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