Question

PLEASE ONLY ANSWER WITH A PROPER ANSWER FOR EACH ONE...NOT JUST FOR POINTS-Thank you so muchhhh

Answer 1

`x > (1)/(2)`

Explanation:

For the first one, in any triangle, we have the sum of two sides is greater than the third side. Hence, we have 3 inequalities:
`4x+3>2x+1, 5x+1>x+3, 3x+4>3x`, which give us
`x>-1, x>(1)/(2),4>0`. We conclude that
`x>(1)/(2)`.

For the second question, we have
`AB<BP+AP=2x`, and similarly we can show that
`AC, BC<2x`. Hence,
`AB+BC+AC<6x`.

The third question is not very clear.