Answer:
x < -2 or x ≥ 2
In interval notation:
(- ∞, 2) ∪ [2, ∞) Notice square bracket next to 2 because the second inequality is a ≥inequality whereas the first inequality is a < inequality
Explanation:
First inequality: 6x - 5 < - 17
Add 5 to both sides:
6x < -17 + 5
6x < -12
Divide both sides by 2 to get
x < -2
In interval notation it is (-∞ , -2) () means neither value is included
Second inequality: 4x + 5 ≥ 13
Subtract 5 from both sides:
4x ≥ 13 -5
4x ≥ 8
Divide both sides by 4:
x ≥ 2
In interval notation [2, ∞) Note square bracket next to 2 which means that value is included. ∞ is never included so it is always accompanied by a ( or ) bracket
Hence we have x < -2 or x >= 2
In interval notation we have (- ∞, 2) ∪ [2, ∞) where the symbol ∪ represents set union which is equivalent to an or
See the attached figure for visual explanation