Answer:
Hence as long as x > 2/3, we can form a triangle from the three given sides.
Step-by-step explanation:
Given:
Length of 3 sides of triangle are [tex]x+3, 4x,3x-1[/tex]
Solution:
From the length of the 2nd side 4x, we know that x > 0
Let this be 1 st statement.
Now from the triangle inequality we can say that;
[tex]x + 3 + 4x > 3x -1\\5x+3>3x-1\\5x-3x>-1-3\\2x>-2\\x>-1[/tex]
No new information from this because of the 1st statement above.
Also,
[tex]4x + 3x - 1 > x +3\\7x-1>x+3\\7x-x>3+1\\6x>4\\x>\frac{4}{6}\\\\x>\frac{2}{3}[/tex]
Lastly,
[tex]x+3 +3x - 1 > 4x\\4x-2>4x\\4x-4x>2\\0>2[/tex]
and again no new information is obtained from this inequality.
Hence as long as x > 2/3, we can form a triangle from the three given sides.
