Question

*A triangle has sides x, x+4 and 3x− 5. What is the possible range of x?

PLease answer like this:
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Answer 1

The length of a side of a triangle must be less than the sum of the lengths of the other two sides. This is called the triangle inequality.
We then can solve the three possible inequalities and see what values satisfy all three simultaneously.
(x) + (x+4) > 3x-5
2x+4 > 3x-5
9 > x
(x+4) + (3x-5) > x
4x-1 > x
3x > 1
x > 1/3
(x) + (3x-5) > x+4
4x-5 > x+4
3x > 9
x > 3
When x is between 3 and 9, the equations are satisfied. This may be shown as
3 < x < 9
or in an interval notation
(3,9)

Answer 2

I hope this will help...

Given a triangle with sides C= x, A= x+4 and B= 3x− 5 the sum of the lengths of any sides of a triangle must be greater than the third side.

1. x + x+4 > 3x-5 2. x+4 + 3x-5 > x 3. x + 3x-5 > x+4
1. x + x+4 > 3x-5 -> x < 92. x+4 + 3x-5 > x -> x < 1/33. x + 3x-5 > x+4 -> x < 3

which implies that the possible range of x is 3 < x < 9