Ответ:

Правило :

если   [tex]\bf |\, x\, | < a[/tex]  ,   то   [tex]\bf -a < x < a[/tex]  .

[tex]\bf |5x-6| < x+1\ \ \ \Rightarrow \ \ \ -(x+1) < 5x-6 < x+1\ \ ,\\\\\left\{\begin{array}{l}\bf 5x-6 < x+1\\\bf 5x-6 > -x-1\end{array}\right\ \ \left\{\begin{array}{l}\bf 5x-x < 6+1\\\bf 5x+x > 6-1\end{array}\right\ \ \left\{\begin{array}{l}\bf 4x < 7\\\bf 6x > 5\end{array}\right\ \ \left\{\begin{array}{l}\bf x < 1\dfrac{3}{4}\\\bf x > \dfrac{5}{6}\end{array}\right\ \ \Rightarrow \\\\\\Otvet:\ \ \boldsymbol{x\in \Big(\ \dfrac{5}{6}\ ;\ 1\dfrac{3}{4}\ \Big)\ .}[/tex]