Geometry homework

Question

Find the value of x. One side of a triangle is the equation 3x+10, and the other side is 6x+1. What is x?

Answer 1

3x + 10 >0 or x>-10/3 if the side >0

6x+ 1 > 0 or x>-1/6 if the other side>0

x > -1/6

Or another way to look at it is consider the maximum length of the 3rd side.

3x + 10 and 6x + 1 sum to 9x +11 which is the maximum length of the 3rd side. IF the 3rd side were any longer, you could not connect all 3 sides into a triangle.

6x + 1 minus 3x + 10 equals 3x - 9

3x + 10 minus 6x + 1 equals 9 - 3x

Either 3x - 9 or 9 - 3x is the minimum length of the 3rd side. If the 3rd side were any smaller, you could not connect all 3 sides into a triangle.

9x + 11 > 3x - 9 the max length of the 3rd side has to be greater than the min length of the 3rd side

6x>-20 subtract 3x from both sides, and subtract 11 from both sides

x>-20/6=-10/3

also 9x + 11 > 9 - 3x add 3x to both sides, and subtract 11 from both sides

12x>-2

x>-2/12=-1/6

So x>-10/3 and x>-1/6 so

x> -1/6