Video Help [+] https//www.xyzhomework.com/imathas/assess2/?cid=37709&aid=2434513#/skip/2 ENTERING INTERVAL ANSWERS For intervals of values, enter your answer using interval notation. Here are some examples of how interval notation relates to inequalities: Inequality Interval Notation 3 < x < 5 (3,5) 3 ? x ? 5 [3,5] x ? 3 (3,?) 3 ? x ? 5 or 7 < x < 9 (3,5) U (7,9) With inequalities, we use “less than”: < or “greater than”: > to exclude the endpoint of the interval. With interval notation, we use use round parentheses, ( or ). With inequalities, we use “less than or equal to”: ? or “greater than or equal to”: ? to include the endpoint of the interval. With interval notation, we use use square brackets, [ or ]. To combine two intervals, use U (an uppercase letter u) for union: U Use oo (two lowercase letter o’s) for infinity, ? For example, to enter (-?, -2) U (3, 6], you would type: (-?,-2]U(3,6) Try it now. Enter the interval equivalent to 2 < x ? 5 or x > 7 Question Help:Message instructor Post to forum Submit 74
The Correct Answer and Explanation is:
To express the inequality 2<x≤52 < x \leq 52<x≤5 or x>7x > 7x>7 in interval notation, we first break down the two conditions and understand how to write them as intervals:
- For 2<x≤52 < x \leq 52<x≤5:
- The inequality says that xxx is strictly greater than 2 but less than or equal to 5.
- In interval notation, this translates to (2, 5]. The round parenthesis around 2 indicates that 2 is not included in the interval, and the square bracket around 5 indicates that 5 is included.
- For x>7x > 7x>7:
- This inequality states that xxx is strictly greater than 7.
- In interval notation, this is written as (7, ∞). The round parenthesis around 7 indicates that 7 is not included in the interval, and the infinity symbol ∞\infty∞ is used to show that there is no upper limit to xxx, so it extends indefinitely.
Since these two inequalities are connected by “or,” we combine them using a union symbol ∪\cup∪. The union means that xxx can be in either of the two intervals.
Thus, the combined interval notation is:(2,5]∪(7,∞)(2, 5] \cup (7, \infty)(2,5]∪(7,∞)
Explanation:
- (2, 5]: This represents the set of values of xxx that are greater than 2 and less than or equal to 5.
- (7, ∞): This represents the set of values of xxx that are greater than 7 and extend indefinitely.
- ∪\cup∪: The union symbol is used to show that xxx can be in either the first interval (2,5](2, 5](2,5] or the second interval (7,∞)(7, \infty)(7,∞).
Therefore, the correct interval notation for 2<x≤52 < x \leq 52<x≤5 or x>7x > 7x>7 is:(2,5]∪(7,∞)(2, 5] \cup (7, \infty)(2,5]∪(7,∞)
This format ensures clarity, representing all values of xxx that satisfy either condition.
