11. Which of the following is a correct graph of x>1, x<4 ?
A. Line segment going from 1 to 4 B. Ray going from 4 to the right and other ray going from 1 to the left C. Ray going from 1 to the right D. Ray going from 4 to the left E. Line segment from 1 to 2 and 4 to 5
Line A
Line B
Line C
Line D
Line E
C. Ray going from 1 to the right
To determine the correct graph for the inequality x>1, x<4, we need to understand the notation and how to represent solutions on a number line.
The inequality x>1 means that x is greater than 1, but not equal to 1. On a number line, we can represent this by drawing an open circle at 1 and extending a line to the right to indicate all the values greater than 1.
The inequality x<4 means that x is less than 4, but not equal to 4. On a number line, we can represent this by drawing an open circle at 4 and extending a line to the left to indicate all the values less than 4.
Now, let's consider the answer options:
A. Line segment going from 1 to 4: This includes the value 4, which violates the inequality x<4.
B. Ray going from 4 to the right and another ray going from 1 to the left: This option correctly represents x>1 and x<4, as it doesn't include 1 or 4.
C. Ray going from 1 to the right: This option only represents x>1 and not x<4.
D. Ray going from 4 to the left: This option only represents x<4 and not x>1.
E. Line segment from 1 to 2 and 4 to 5: This includes 2 and 5, violating both x>1 and x<4.
Based on the above explanations:
The correct graph for x>1, x<4 is Line B: A ray going from 4 to the right and another ray going from 1 to the left.