Question

Which inequality represents the value of x that ensures triangle abc exists?

Answer 1

awnser Is A

Explanation:

because

Answer 2

Option A.

Explanation:

According to triangle inequality theorem, a triangle exists if the sum of two sides is greater that third side.

Apply this theorem on each combination.

Case I:
`(2x+4)+6x>18`

`8x+4>18`

`8x>14`

`x>(14)/(8)`

`x>(7)/(4)` ...(1)

Case II:
`(2x+4)+18>6x`

`2x+22>6x`

`22>4x`

`(22)/(4)>x`

`(11)/(2)>x` ...(2)

Case III:
`6x+18>2x+4`

`6x-2x>4-18`

`4x>-14`

`x>-(14)/(4)`

`x>-(7)/(2)` ...(3)

On combining (1), (2) and (3), we get

`(7)/(4)<x<(11)/(2)`

Therefore, the correct option is A.