Answer:
n = 8 or n = −6
Explanation:
First, isolate the absolute value:
5 − |n − 1| = −2
7 − |n − 1| = 0
7 = |n − 1|
Then, split this into two equations, since the result of the absolute value could be positive or negative:
7 = n − 1 7 = −(n − 1)
8 = n 7 = −n + 1
n = −6
Answer:
[tex]\{-6\} \cup \{8\}[/tex]
Step-by-step explanation:
[tex]5 - |n - 1| = -2; \\ -|n - 1| = -2 - 5 \\ -|n - 1| = -7 \\ |n - 1| = 7 \\ \left \ [ {{n - 1 = 7} \atop {n - 1 = -7}} \right. \Leftrightarrow \left \ [ {{n = 7 + 1} \atop {n = -7 + 1}} \right. \Leftrightarrow \left \ [ {{n = 8} \atop {n = -6}} \right.[/tex]
