Graph on a number line: open circles at 2 and 4, line segment between, represents x.
The set notation 2 less than x less than 4 represents the set of all real numbers x that satisfy the inequality 2 < x < 4. This notation describes an open interval between 2 and 4 on the number line, excluding the endpoints.
To graph this on a number line:
1. Locate the point representing 2 and mark it with an open circle to indicate that it is not included in the set.
2. Similarly, locate the point representing 4 and mark it with an open circle as it's also not included.
3. Draw a line segment between these points to represent all the numbers greater than 2 and less than 4.
In the notation 2 less than x less than 4, the inequality 2 < x < 4specifies that the set includes all real numbers x that are greater than 2 but less than 4. Therefore, any value between 2 and 4 but not including 2 and 4 themselves would be part of this set.
Visually, the graphed number line would show an open interval starting at 2 (excluded) and ending at 4 (excluded), indicating the range of numbers satisfying the inequality 2 < x < 4. The shaded segment between 2 and 4 would represent the set x on the number line.