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tangare [24]
2 years ago
9

Find the range of possible measures of x if each set of expressions represents measures of the sides of a triangle.

Mathematics
1 answer:
sergiy2304 [10]2 years ago
8 0

Answer:

  • C. x > 3/2

Step-by-step explanation:

<u>According to the triangle inequality theorem, any side length is less than the sum of the other two:</u>

  • x < 2x + 1 + x + 4 ⇒ x < 3x + 5 ⇒ 2x > - 5 ⇒ x > - 2.5
  • 2x + 1 < x + x + 4 ⇒ 2x + 1 < 2x + 4 ⇒ 1 < 4, any value of x
  • x + 4 < x + 2x + 1 ⇒ x + 4 < 3x + 1 ⇒ 2x > 3 ⇒ x > 3/2

<u>Common solution of the three inequalities above is:</u>

  • x > 3/2

Correct choice is C

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