Write the given inequality using interval notation, and illustrate the inequality using the real number line.
-1≤x≤2
Use interval notation to express the inequality. What is the resulting interval?
Answer (2)
The inequality − 1 ≤ x ≤ 2 means x is between -1 and 2, inclusive.
Use square brackets to include the endpoints in interval notation.
The interval notation is [ − 1 , 2 ] .
The resulting interval is [ − 1 , 2 ] .
Explanation
Understanding the Inequality We are given the inequality − 1 ≤ x ≤ 2 . This means that x can be any value between -1 and 2, including -1 and 2. We need to express this inequality using interval notation.
Using Interval Notation In interval notation, we use square brackets to indicate that the endpoints are included in the interval. Since x can be equal to -1 and 2, we will use square brackets for both endpoints.
Writing the Interval The interval notation for the inequality − 1 ≤ x ≤ 2 is [ − 1 , 2 ] . This means that the interval starts at -1 and ends at 2, and both -1 and 2 are included in the interval.
Examples
Interval notation is used in various fields, such as calculus and real analysis, to represent sets of real numbers. For example, when describing the domain or range of a function, interval notation provides a concise way to specify the set of possible input or output values. In everyday life, you might use interval notation to describe a range of acceptable temperatures for a certain process or the duration of an event.
The inequality − 1 ≤ x ≤ 2 can be expressed in interval notation as [ − 1 , 2 ] , indicating that x can take any value from − 1 to 2 , inclusive. On a number line, this is illustrated with solid dots at − 1 and 2 and shading between them. Thus, the resulting interval is [ − 1 , 2 ] .
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