Final answer:
To solve the inequalities 3x≤-6 or x-2>0, we solve each separately. The interval notation for x≤-2 is [-2, ∞) and for x>2 is (2, ∞). Combining both we get (-∞, -2] ∪ (2, ∞), meaning x is either ≤ -2 or > 2.
Step-by-step explanation:
Interval Notation for Inequalities
To solve the inequalities 3x≤-6 or x-2>0, we need to treat each inequality separately and then combine the solutions.
For the first inequality, divide both sides by 3 to isolate x:
3x≤-6 → x ≤ -2
In interval notation, this solution is [-2, ∞).
For the second inequality, add 2 to both sides to isolate x:
x-2>0 → x>2
In interval notation, this solution is (2, ∞).
Since the original statement uses 'or', we combine the intervals:
(-∞, -2] ∪ (2, ∞)
This means x is less than or equal to -2 or greater than 2.