Answer:
11 < x < 35
Explanation:
In a triangle, the sum of the lengths of any two sides must be greater than the length of the third side. Using this property, we can write the inequality to find the possible values of x:
For the given triangle with sides measuring 12, 23, and x:
12 + 23 > x
12 + x > 23
23 + x > 12
Combining all three inequalities, we get:
12 + 23 > x and 12 + x > 23 and 23 + x > 12
Solving each inequality:
12 + 23 > x
35 > x
12 + x > 23
x > 23 - 12
x > 11
23 + x > 12
x > 12 - 23
x > -11
So, the possible values of x are such that x is greater than 11 and less than 35:
11 < x < 35