Question

Which inequality represents the values of X that insure triangle ABC exists

Answer 1

Answer:

7/4 < x < 11/2

Step-by-step explanation:

I think your question is missed of key information, allow me to add in and hope it will fit the original one.  

Please have a look at the attached photo.  

My answer

Given the information:

• AB: 2x + 4
• BC: 6x
• AC: 16

All of these three triangle inequalities must be satisfied:

•  AB +BC > AC

<=> 2x + 4 + 6x > 18

<=> 8x > 14

<=> x > 7/4

•  BC +CA > BA

6x + 18 > 2x + 4

<=> 4x > -14

<=> x > -14/4

•  CA +AB > CB

18 + 2x + 4 > 6x

<=> 22 > 4x

<=> x < 11/2

So the inequality represents the values of X that insure triangle ABC exists is:  7/4 < x < 11/2

Hope it will find you well.