Which graph represents the compound inequality? –3 < n < 1

General
1

Which graph represents the compound inequality?

–3 < n < 1

2

Which graph represents the compound inequality –3 < n < 1?

To determine which graph represents the compound inequality -3 < n < 1, we need to consider the following key points associated with this type of inequality:

  1. Understanding the Inequality:

    • The inequality -3 < n < 1 indicates that n is any number that is greater than -3 and less than 1.
    • This means n lies strictly between -3 and 1 but does not include -3 or 1.

  2. Interval Notation:

    • In interval notation, this compound inequality can be written as (-3, 1).
    • The parentheses indicate that the endpoints -3 and 1 are not included in the interval.

  3. Graph Representation:

    • On a number line, the inequality -3 < n < 1 would be represented as an open interval from -3 to 1.
    • Open circles (or hollow dots) are placed at -3 and 1 on the number line to show that these points are not included.

  4. Drawing the Graph:

    • Draw a number line.
    • Place open circles at -3 and 1.
    • Shade the portion of the number line that lies between -3 and 1.

Here is a visualization of the graph:

---|----|----|----|----|----|----|----
  -4   -3   -2   -1    0    1    2

(Open circle at -3 and 1, shaded region between -3 and 1)

In summary, the graph representing the inequality -3 < n < 1 will be a number line with open circles at -3 and 1, and the portion of the line between these points shaded to indicate all the numbers between -3 and 1.

If the graph you are looking at matches this description, then it accurately represents the compound inequality -3 < n < 1. If you have multiple given graphics, choose the one showing open circles at -3 and 1, with the segment between them shaded.