To solve the compound inequality we need to solve each inequality, then we have:
[tex]\begin{gathered} 3x+5>23\text{ or }4x-4\leq0 \\ 3x>23-5\text{ or }4x\leq0+4 \\ 3x>18\text{ or }4x\leq4 \\ x>\frac{18}{3}\text{ or }x\leq\frac{4}{4} \\ x>6\text{ or }x\leq1 \end{gathered}[/tex]
Now we need to remember that the word OR means the union of the solution sets for each inequality then the solution is:
[tex](-\infty,1\rbrack\cup(6,\infty)[/tex]
