Answered

At Westonci.ca, we connect you with the answers you need, thanks to our active and informed community. Get detailed answers to your questions from a community of experts dedicated to providing accurate information. Get immediate and reliable solutions to your questions from a community of experienced professionals on our platform.

What are the absolute value answers to 5n+24=|8-3n|?

Sagot :

konrad509
[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]
naǫ
[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]
We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. Westonci.ca is your go-to source for reliable answers. Return soon for more expert insights.