Choice A is the correct answer. Split into cases.
- Case 1: 2x−5>3x→−5>x→x<−5
- Case 2: 2x−5<−3x→5x<5→x<1
- Combine: The union of x<−5 and x<1 is x<1 (since x<−5 is inside x<1).
- Check x=0: ∣−5∣>0 (5>0) True.
- Check x=−6: ∣−17∣>−18 (17>-18) True.
- Check x=2: ∣−1∣>6 (1>6) False.
Wait, let's re-evaluate carefully.
∣A∣>B is A>B or A<−B.
- 2x−5>3x→−x>5→x<−5
- 2x−5<−3x→5x<5→x<1
Union: x<1 OR x<−5. The set x<1 includes x<−5. So x<1.
Let's check x=0.9: ∣1.8−5∣=3.2>2.7. True.
Let's check x=−10: ∣−25∣=25>−30. True.
So x<1 seems correct.
Choice A is correct.Choice B is incorrect (subset).
Choice C is incorrect.
Choice D is incorrect.