What type of interval does the following inequality represent?
−10 ≤ x < −6
is this an open, close or half open
need help
closed on the left, open on the right
Better review what the inequality signs mean...
Well, this inequality represents a closed interval. Why? Because the inequality uses '≤' (less than or equal to) for the lower bound and '<' (less than) for the upper bound. The inclusion of the equal sign in the lower bound makes it a closed interval. So, it would be like standing outside, but just barely not getting in the party.
The inequality −10 ≤ x < −6 represents a half-open interval.
In a half-open interval, one endpoint is included, and the other is not. In this case, the endpoint −10 is included (≤ symbol), and the endpoint −6 is not included (< symbol).
To determine the type of interval represented by the inequality −10 ≤ x < −6, you can break it down into two parts: the left side (−10 ≤ x) and the right side (x < −6).
On the left side, we have the inequality −10 ≤ x. This represents a closed interval because it includes the value of −10. A closed interval is denoted by using square brackets [ ].
On the right side, we have the inequality x < −6. This represents an open interval because it does not include the value of −6. An open interval is denoted by using parentheses ( ).
To combine both sides, we use the symbols for "and" ( ∧ ) or "intersection" (∩). Thus, the overall type of interval represented by the inequality −10 ≤ x < −6 is a half-open interval. In interval notation, it can be written as [-10, -6) or using set notation as {x | -10 ≤ x < -6}.