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Magazine Chapter 2: Q. 432 (page 288)
In the following exercise, graph each inequality on the number line
鈸� x 鈮� 鈭�3 鈸� x < 4 鈸� x 鈮� 鈭� 2
Short Answer
The required graphs are as shown below:
Step by step solution
Step 1. Given information
The inequalities given are:
鈸� x 鈮� 鈭�3
鈸� x < 4
鈸� x 鈮� 鈭� 2
We have to plot the graph of the given inequalities.
Part (a) Step 1. Plotting the inequality x ≥ −3.
Now,
x 鈮� 鈭�3 means all numbers greater than or equal to -3.
Therefore, we shade in all the numbers on the number line to the right of -3 and put a solid circle at x = -3 to show that it is included.
The graph will be as shown below.
Part (b) Step 1. Plotting the inequality x < 4.
x < 4 means all numbers less than 4, but not including 4.
Therefore, we shade in all the numbers on the number line to the left of 4 and put a hollow circle at x = 4 to show it is not included.
Part (c) Step 1. Plotting the inequality x ≤ − 2.
Now,
x 鈮� 鈭� 2 means all numbers less than or equal to -2.
Therefore, we shade in all the numbers on the number line to the left of -2 and put a solid circle at x = -2 to show that it is included.
The graph will be as shown below.
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