A man $($mass $=76kg)$ is standing on a beam of length $L=5m$ supported by two cables $($one on the left, one on the right$).$ The right$-$hand cable is offset from the end of the beam by a fraction $a=0\mathrm{.}19$ of the beam length. The man is standing a distance x from the left$-$hand side of the beam. The beam's mass is $107$ kg $.$ The problem for the man is that the two cables are fairly weak and could easily snap. The maximum safe tension for the left beam is $0\mathrm{.}9{10}^{3}N$ while the maximum safe tension for the right beam is $1\mathrm{.}1{10}^{3}N.$ If x is too small or too large, one $-$ff the cables will likely fail. What is the range of motion of the man to safely walk along the beam $(x_{\text{m}\text{a}\text{x}}-x_{\text{m}\text{i}\text{n}})?$

Your answer should be in $m,$ but enter only the numerical part in the box.