Answer:
1.3 < x < 6.7
Step-by-step explanation:
You want the possible length of the third side of a triangle with sides 2.7 and 4.0.
Triangle inequality
The triangle inequality tells you the sum of any two sides must exceed the third side. In practice, that means the sum of the two shorter sides is greater than the longest side.
There are three possibilities, of which two place limits on the length of x.
X is the shortest side
This means ...
x +2.7 > 4
x > 1.3 . . . . . . . subtract 2.7
X is the longest side
This means ...
2.7 +4.0 > x
6.7 > x
Compound inequality
Writing these limits as a compound inequality, we have ...
1.3 < x < 6.7
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Additional comment
You will notice these limits are the difference and sum of the given side lengths.
The third possibility is that x is the middle-length side, between 2.7 and 4.0. That possibility is included in the range shown above.
