Answer :

[tex]x-the\ number\\\\\frac{5}{6}x+7 > -3\ \ \ \ \ |-7\\\\\frac{5}{6}x > -3-7\\\\\frac{5}{6}x > -10\ \ \ \ \ |\times\frac{6}{5}\\\\x > -2\times6\\\\x > -12\\\\x\in(-12;\ \infty)[/tex]