Answer:
x > 1/5
Explanation:
All of these three triangle inequalities must be satisfied:
AB +BC > AC
BC +CA > BA
CA +AB > CB
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Taking these one at a time, we have ...
AB +BC > AC
3x +4 + 2x +5 > 4x
x +9 > 0 . . . . . subtract 4x
x > -9
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BC +CA > BA
2x +5 + 4x > 3x +4
3x > -1 . . . . . . subtract 3x+5
x > -1/3 . . . . . divide by 3
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CA + AB > CB
4x + 3x +4 > 2x +5
5x > 1 . . . . . . subtract 2x+4
x > 1/5
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The only values of x that satisfy all of these inequalities are those such that ...
x > 1/5