\(\begin{array}{1}{x^2}  x  56 \ge 0\\(x + 7)(x  8) \ge 0\end{array}\)
\(\left\{ \begin{array}{l}x + 7 \ge 0\\x  8 \ge 0\end{array} \right.\) or \(\left\{ \begin{array}{l}x + 7 \le 0\\x  8 \le 0\end{array} \right.\)
\(\left\{ \begin{array}{l}x \ge  7\\x \ge 8\end{array} \right.\) or \(\left\{ \begin{array}{l}x \le  7\\x \le 8\end{array} \right.\)
\(x \ge 8\) or \(x \le  7\)
Therefore,the solutions of the inequality are \(x \le  7\) or \(x \ge 8\).
Alternative method:
\(\begin{array}{c}{x^2}  x  56 \ge 0\\(x + 7)(x  8) \ge 0\end{array}\)
Construct the following table to show the signs of the expressions of
\(x + 7\), \(x  8\) and \((x + 7)(x  8)\) in the relevant intervals of x.

 \(x <  7\)  \(x =  7\)  \(  7 < x < 8\)  \(x = 8\)  \(x > 8\) 
\(x + 7\)    0  +  +  + 
\(x  8\)        0  + 
\((x + 7)(x  8)\)  +  0    0  + 
According to the table above,
the solutions of the inequality are \(x \le  7\) or \(x \ge 8\).