Answer:
-5 < x-1 < 5
Step-by-step explanation:
Consider |a|. This has the value -a when a < 0. So, if we write the inequality ...
|a| < b
it is equivalent to two inequalities:
a < b . . . . for a ≥ 0
-a < b . . . for a < 0
Multiplying by -1. the latter inequality is ...
a > -b . . . for a < 0
Written using the < symbol, this is ...
-b < a
So, the original inequality can be written as the two inequalities ...
-b < a (for a < 0) or a < b (for a ≥ 0)
Since these are disjoint, we can form their union as ...
-b < a < b
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Above, we have a = x-1, b = 5, so the inequality |x-1| < 5 can be written ...
-5 < x -1 < 5
