Enter the interval equivalent to 2 < x ≤ 5 or x > 7
(2,5] U (7,∞)
Sure, I'd be happy to provide an interval equivalent to the given inequality.
How about we represent it as (2, 5] U (7, ∞) with the parentheses denoting exclusive endpoints and the square brackets denoting inclusive endpoints? This way, it includes all real numbers greater than 2 but less than or equal to 5, as well as all real numbers greater than 7. It's quite the interval, isn't it? Like a lively circus tent filled with numbers!
To find the interval equivalent to the inequality 2 < x ≤ 5 or x > 7, we need to merge the two separate intervals into one.
First, let's look at the interval 2 < x ≤ 5.
- The inequality 2 < x means x is greater than 2, but not equal to 2. So, we can write this as x > 2.
- The inequality x ≤ 5 means x is less than or equal to 5.
Combining these two conditions, we get the interval (2, 5].
Now, let's consider the interval x > 7.
- The inequality x > 7 means x is greater than 7.
So, the interval x > 7 can be written as (7, ∞).
Finally, to merge the two intervals together, we can use the union symbol (∪).
Therefore, the interval equivalent to 2 < x ≤ 5 or x > 7 is (2, 5] ∪ (7, ∞).
To find the interval equivalent to the given compound inequality 2 < x ≤ 5 or x > 7, we need to combine the separate intervals and express them using interval notation.
First, let's consider the interval 2 < x ≤ 5. This means that x is greater than 2 but less than or equal to 5. To represent this interval in interval notation, we write (2, 5].
Next, let's consider the interval x > 7. This means that x is greater than 7. In interval notation, this can be represented as (7, ∞).
To combine both intervals, we use the union symbol (∪). So, the interval equivalent to the given compound inequality is (2, 5] ∪ (7, ∞). This implies that x can be any value between 2 (excluding 2) and 5 (including 5), or any value greater than 7.