Sagot :
[tex]5n+24=|8-3n|\\
5n+24\geq0\\
5n\geq-24\\n\geq-\dfrac{24}{5}\\
8-3n=5n+24 \vee 8-3n=-5n-24\\
8n=-16 \vee 2n=-32\\
n=-2 \vee n=-16\\\\
-16\not\geq-\dfrac{24}{5} \Rightarrow \boxed{n=-2}[/tex]
[tex]\hbox{the domain:} \\
5n+24 \geq 0 \\
5n \geq -24 \\
n \geq -\frac{24}{5} \\
n \geq -4 \frac{4}{5}[/tex]
[tex]5n+24=|8-3n| \\ 5n+24=8-3n \ \lor \ -(5n+24)=8-3n \\ 5n+3n=8-24 \ \lor \ -5n-24=8-3n \\ 8n=-16 \ \lor \ -5n+3n=8+24 \\ n=-2 \ \lor \ -2n=32 \\ n=-2 \ \lor \ n=-16[/tex]
[tex]n=-2 \geq -4 \frac{4}{5} \hbox{ - it is a solution} \\ n=-16 < -4 \frac{4}{5} \hbox{ - it isn't a solution} \\ \\ \boxed{n=-2}[/tex]
[tex]5n+24=|8-3n| \\ 5n+24=8-3n \ \lor \ -(5n+24)=8-3n \\ 5n+3n=8-24 \ \lor \ -5n-24=8-3n \\ 8n=-16 \ \lor \ -5n+3n=8+24 \\ n=-2 \ \lor \ -2n=32 \\ n=-2 \ \lor \ n=-16[/tex]
[tex]n=-2 \geq -4 \frac{4}{5} \hbox{ - it is a solution} \\ n=-16 < -4 \frac{4}{5} \hbox{ - it isn't a solution} \\ \\ \boxed{n=-2}[/tex]