✅ Corrigé — Exercice 3

1) |x − 4| ≤ 3 → x ∈ [4−3 ; 4+3] = [1 ; 7].

2) |x + 2| < 5 → |x − (−2)| < 5 → x ∈ ]−2−5 ; −2+5[ = ]−7 ; 3[.

3) |2x − 1| ≤ 7 → −7 ≤ 2x−1 ≤ 7 → −6 ≤ 2x ≤ 8 → x ∈ [−3 ; 4].

4) |3x + 6| < 9 → |3(x+2)| < 9 → |x+2| < 3 → x ∈ ]−2−3 ; −2+3[ = ]−5 ; 1[.

5) d(−7, 2) = |2−(−7)| = 9. d(1/3, 1/2) = |1/2 − 1/3| = |3/6 − 2/6| = 1/6.

6) Distance au plus 3 de −1 : |x − (−1)| ≤ 3 → |x + 1| ≤ 3 → x ∈ [−4 ; 2].