Posted by **Nina** on Thursday, June 23, 2011 at 8:49am.

If the sides of a triangle have measurements 3x + 4 , 6x - 1, and 8x + 2, find all possible values of x.

I also need help with this question please

- Geometry Help!!!!!!!!!! -
**Anonymous**, Thursday, June 23, 2011 at 9:01am
All sides must be greater of zero.

3x+4 always>0

8x+2 always>0

Only side: 6x-1 can be negative.

That's why:

6x-1>0

6x>1 Divide both sides with 6

x>1/6

- Geometry Help!!!!!!!!!! -
**Nina**, Thursday, June 23, 2011 at 9:10am
Thanks anyway but that isn't one of the choices the answer is x> 3/11 i figured it out thanks for trying :)

- Geometry Help!!!!!!!!!! -
**Istan**, Thursday, June 23, 2011 at 9:15am
Anonymus solution not completely.

All sides must be greater of zero:

3x+4>0

3x> -4 Divide with 3

x> -4/3

6x-1>0

6x>1 Divide with 6

x>1/6

8x+2>0

8x> -2 Divide with 8

x> -2/8

x> -1/4

Least of that numbers is -4/3= -1.3333

x> -4/3 is solution

- Geometry Help!!!!!!!!!! -
**Istan**, Thursday, June 23, 2011 at 9:24am
x>3/11 is also > -4/3

All x> -4/3 is choices

- Not correct - Geometry Help!!!!!!!!!! -
**Reiny**, Thursday, June 23, 2011 at 9:26am
The condition that all sides have to be positive, as Anonymous used, is not sufficient.

In any triangle the sum of 2 sides must be greater than the third side, so

3x+4 + 6x-1 > 8x + 2 ----> x > -1

AND

3x+4 + 8x + 2 > 6x-1 ---> x > -7/5

AND

8x + 2 + 6x - 1 > 3x+4 --> x > 3/11

the intersection of all three conditions is

x > 3/11

To show that Anonymous is incorrect, pick a value of x between his/her answer of 1/6 and mine of 3/11

e.g. x = 11/50

3x+4 --> 4.66

6x-1 --> .32

8x+2 --> -.24 , contradiction

I have a value of x > 1/6 which did not work.

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