|-2x+1|<3 — step-by-step solution

Let's solve in

ℝ

| - 2 x + 1 | < 3

| A | < B

is equivalent to

- B < A < B

-3 < - 2 x + 1 < 3

Add

-1

to all three parts of the inequality

-4 < - 2 x < 2

We divide all three parts by

-2

, which is negative: both inequality signs reverse

-1 < x < 2

▶Solution obtained:

x \in (-1, 2)