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To express the set of real numbers x that satisfies the inequality -2 ≤ x < 5, we used the Interval notation method and got the solution set as [-2,5).

Interval Notation Method :

Interval notation is a way of representing intervals on the number line. That is, how to write a subset of the real number line. Intervals include numbers between two specific numbers. We can use this notation to express inequalities.

Generally, we read about the three types of intervals :

  • Open intervals : This type of interval does not contain the endpoints of the inequality. For example, for set {x | -a< x < b}, the open interval notation is (-a, b).
  • Closed Intervals: This type of interval contains the endpoints of the inequalities. For example, for set {x | -a≤ x ≤ b} the closed interval notation is [-3,1].
  • Half-Open Interval: This type of interval contains only one endpoint of the inequality. For example, for set {x| -a ≤ x < b} the half-open interval notation is [-3,1).

We have given an inequality as -2 ≤ x < 5

We have to express the set of real numbers x that satisfies the given inequality.

Let's started, The first thing we'll want to ask ourselves is if we're going to use parentheses or brackets when we write this.

y = { x | -2 ≤ x < 5 }

We see that the lower value of x is -2 or greater than -2 and higher value of x is less than 5. We're just going to write it down. Using the interval notation, the lower side x is greater than and equal to -2 so, we use closed bracket here and the upper side x is less than 5 that is we use parentheses or open bracket here.

Thus, in interval notation y = x , x∈[-2, 5)

To learn more about Interval notation, refer:

https://brainly.com/question/26025356

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