Question

5-|n-1|=-2

| | stands for absolute value

Answer 1

`\{-6\} \cup \{8\}`

Step-by-step explanation:

`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.`

Answer 2

n = 8 or n = −6

Step-by-step 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