Question

Find the solution of [x - 1 ] ≤5, [x]≥2?​

Answer 1

Consider the inequality, ∣x−1∣+∣x+2∣≥3

⟹x−1+x+2≥3 and x−1+x+2≤−3

⟹2x+1≥3 and 2x+1≤−3

⟹2x≥3−1 and 2x≤−3−1

⟹2x≥2 and 2x≤−4

⟹x≥1 and x≤−2

The solution set is,

From x≥1 we get [1,∞)

From x≤−2 we get (−∞,−2]