Triangle has sides 7 inches, 7.5 inches, and x inches. What is the range of possible lengths for side x, in inches? A. 0.5 x>14.5

C. 0.5≥x≥14.5

D.0.5≤x≤14.5

The  range of possible lengths for side x, in inches is 0.5 < x < 14.5

Using the triangular law which states that the sum of any two sides must be greater than the third.

x + y > z

y + z > x

x + z > y

From the equations above;

x > z - y and y + z > x

z-y < x < y+z

Let y = 7 and z = 7.5

7.5 - 7 < x < 7 + 7.5

0.5 < x < 14.5

Hence the  range of possible lengths for side x, in inches is 0.5 < x < 14.5

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0.5 < x < 14.5

Step-by-step explanation:

Triangle Inequality Theorem

Let y and z be two of the side lengths of a triangle. The length of the third side x cannot be any number. It must satisfy all the following restrictions:

x + y > z

x + z > y

y + z > x

Combining those inequalities, and provided y>z, the third size must satisfy:

y - z < x < y + z

We are given two of the triangle side lengths as y=7.5 and z=7, thus the third side length (x) can be in the range:

7.5 - 7 < x < 7.5 + 7

0.5 < x < 14.5

Note: The latter is the correct answer but none of the choices is accurate. Choice D is closer to the correct answer but the endpoints cannot be included.

225x²+4=0

225x²=0-4

225x²=-4

x²=-4/225

x=±√-4/225