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Chapter 1: Q2. (page 43)

OPEN-ENDED: Write a compound inequality whose graph is the empty set.

Short Answer

Expert verified

The compound inequality whose graph is empty set is x鈮�10and -3x鈮�6.

Step by step solution

01

– Define the inequalities 

Let a variable x.

Let the inequality for at least situations is x鈮�10and -3x鈮�6.

02

– Rewrite the inequalities to as a compound inequality with word and 

Inequality for at least situation is x鈮�10, and -3x鈮�6

Now, use the word 鈥榓nd鈥� and write the compound inequality then solve each inequality as follows:

x鈮�10 and -3x鈮�6

x鈮�10and -x鈮�2

x鈮�10and x鈮�-2

Since the intersection 鈥榓nd鈥� contains only the elements that belong to both sets, therefore the compound inequality is x鈮�10 and x鈮�-2.

03

– Draw the graph for the compound inequality

The graph for the compound inequality is x鈮�10andx鈮�-2is shown below:

Therefore, the shaded line with violet colour is an empty set.

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