What is |2x-6|-|x-2|<= |2x-4|-|x-3| ?

The solution to |2x-6|-|x-2| = 5/2

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|2x-6|-|x-2|<= |2x-4|-|x-3|

∣ 2 x - 6 ∣ - ∣ x - 2 ∣ \leq ∣ 2 x - 4 ∣ - ∣ x - 3 ∣

x \geq \frac{5}{2}

Solution steps

∣ 2 x - 6 ∣ - ∣ x - 2 ∣ \leq ∣ 2 x - 4 ∣ - ∣ x - 3 ∣

Find positive and negative intervals

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

Solve the inequality for each interval

No Solution or \frac{5}{2} \leq x < 3 or x \geq 3

Merge Overlapping Intervals

x \geq \frac{5}{2}

8 x < 96

\frac{x - 6}{4} \leq 4

- 27 x^{3} + 64

\frac{2 - x}{3} + 30 = 24

x^{2} = 2 - x

What is |2x-6|-|x-2|<= |2x-4|-|x-3| ?
The solution to |2x-6|-|x-2|<= |2x-4|-|x-3| is x>= 5/2