compound inequalities And Or Intersection Unio
-16 ≤ 2 + 9x ≤ 11
12 – x > 15 or 4x – 13 > 7
-16 ≤ 2 + 9x ≤ 11, this gives rise to two inequalities, viz.
-16 ≤ 2 + 9x and 2 + 9x ≤ 11
rearranging both inequalities,
- 16 - 2 ≤ 9x and 9x ≤ 11 - 2
- 18 ≤ 9x and 9x ≤ 9
- 2 ≤ x and x ≤ 1
i.e. x lies in the range defined by: - 2 ≤ x ≤ 1
12 – x > 15 or 4x – 13 > 7
rearranging both inequalities gives,
12 - 15 > x or 4x > 7 + 13
-3 > x or 4x > 20
i.e. x < -3 or x > 5