Answer:
1 < x < 19
Explanation:
Given triangle sides of 9, 10, and x, you want an inequality that describes the allowed values of x.
Triangle inequality
The triangle inequality requires the sum of any two side lengths exceed the length of the third side. Here, that means we require ...
9 +x > 10 ⇒ 1 < x
9 + 10 > x ⇒ x < 19
Combining these into a single inequality, we have ...
1 < x < 19
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Additional comment
The third inequality is 10 + x > 9, or x > -1. The requirement x > 1 is more restrictive.
In effect, the length of the third side must lie between the sum and difference of the lengths of the other two sides.
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