|3x-5| ≤ |2x-3| - |4x-6|
⇔ |4x-6| - |2x-3| ≤ 3x-5 ≤ |2x-3| - |4x-6|
⇔ |4x-6| - |2x-3| ≤ 3x-5 ∧ 3x-5 ≤ |2x-3| - |4x-6|
⇔ |4x-6| ≤ 3x-5 + |2x-3| ∧ |4x-6| ≤ |2x-3| - (3x-5)
⇔ -(3x-5) - |2x-3| ≤ 4x-6 ≤ 3x-5 + |2x-3|
∧ 3x-5 - |2x-3| ≤ 4x-6 ≤ |2x-3| - (3x-5)
⇔ -(3x-5) - |2x-3| ≤ 4x-6 ∧ 4x-6 ≤ 3x-5 + |2x-3|
∧ 3x-5 - |2x-3| ≤ 4x-6 ∧ 4x-6 ≤ |2x-3| - (3x-5)
⇔ |2x-3| ≥ -(4x-6) - (3x-5) ∧ |2x-3| ≥ 4x-6 - (3x-5)
∧ |2x-3| ≥ 3x-5 - (4x-6) ∧ |2x-3| ≥ 4x-6 + (3x-5)
⇔ [(4x-6) + (3x-5) ≥ 2x-3 ∨ 2x-3 ≥ -(4x-6) - (3x-5)]
∧ [3x-5 - (4x-6) ≥ 2x-3∨2x-3 ≥ 4x-6 - (3x-5)]
∧ [4x-6 - (3x-5) ≥ 2x-3 ∨ 2x-3 ≥ 3x-5 - (4x-6)]
∧[-(4x-6) - (3x-5) ≥ 2x-3 ∨ 2x-3 ≥ 4x-6 + (3x-5)]
⇔ (x ≥ 8/5 ∨ x ≥ 14/9)
∧ (x ≤ 4/3 ∨ x ≥ 2)
∧ (x ≤ 2 ∨ x ≥ 4/3)
∧ (x ≤ 14/9 ∨ x ≤ 4/3)
⇔ (x ≥ 14/9) ∧ (x ≤ 4/3 ∨ x ≥ 2) ∧ (x ≤ 2 ∨ x ≥ 4/3) ∧ x ≤ 14/9
⇔ x = 14/9 ∧ (x ≤ 4/3 ∨ x ≥ 2) ∧ (x ∈ ℝ̲)
⇔ x ∈ {14/9} ∩ ((-∞, 4/3) ∪ (2, +∞))
⇒ x ∈ ∅
