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In triangle ABC, determine the possible values for x. Triangle ABC has side lengths 15, 3, and 2x - 4.

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Final answer:

The range of possible values for x in triangle ABC, taking into account the Triangle Inequality Theorem and ensuring the side lengths are positive, is 2 < x < 11.

Step-by-step explanation:

Determining the Possible Values for x in a Triangle

To determine the possible values for x in triangle ABC with side lengths 15, 3, and 2x - 4, we must use the Triangle Inequality Theorem. The Triangle Inequality Theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. Therefore, we have two inequalities to consider:

  • 15 + 3 > 2x - 4
  • 15 + (2x - 4) > 3

To find the range of possible values for x, we will solve each inequality:


  1. 15 + 3 > 2x - 4
    18 > 2x - 4
    22 > 2x
    11 > x

  2. 15 + 2x - 4 > 3
    2x + 11 > 3
    2x > -8
    x > -4

Combining these inequalities, we find that the possible values for x are:

-4 < x < 11.

However, we must consider the third side which is not in the inequality. For x to be positive and the side to have a positive length, x must be greater than 2. Therefore, the final possible range for x, considering all sides of the triangle, is:

2 < x < 11.

User JeremiahB
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