Respuesta :

mhanifa

Answer:

  • x > 14

Step-by-step explanation:

Use the triangle inequality which states that for any triangle, the sum of the lengths of any two sides must be greater than to the length of the remaining side.

  • FH < FG + GH ⇒ 2x + 31 < 2x + 1 + x + 16 ⇒ x > 14
  • FG < FH + GH ⇒ 2x + 1 < 2x + 31 + x + 16 ⇒ x > - 46
  • GH < FH + FG ⇒ x + 16 < 2x + 31 + 2x + 1 ⇒ x > - 16/3

Combine the above three inequalities:

  • x > 14
DarlinEsteves

Answer:

[tex]x > 14[/tex]

Step-by-step explanation:

By triangle inequality;

[tex]2x + 1 + x + 16 > 2x + 31 \\ 2x + x - 2x > 31 -17 \\ x > 14[/tex]

The possible values of x is any number above 14, that is, x=[ 15, 16, 17, 18, .....}, if x is integer.

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