Which of the following is equivalent to |x-1| <5? X-1<5
5< x-1 <5
-5 < x-1 < 5
-5> x-1 < 5

  -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