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Answer:
15/7 < x < 13
Step-by-step explanation:
The triangle inequality requires that side lengths a, b, c satisfy ...
a + b > c
a + c > b
b + c > a
These can let us write three inequalities for the side lengths given:
6x -11 +3x -1 > 2x +3 ⇒ 7x > 15
6x -11 +2x +3 > 3x -1 ⇒ 5x > 7
3x -1 +2x +3 > 6x -11 ⇒ x < 13
The first two resolve to ...
x > 15/7 ≈ 2.143
x > 7/5 = 1.4
So, the final requirement is that ...
15/7 < x < 13
