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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 $x \geq 10$ and $- 3 x \geq 6$ .

Step by step solution

01

– Define the inequalities

Let a variable $x$ .

Let the inequality for at least situations is $x \geq 10$ and $- 3 x \geq 6$ .

02

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

Inequality for at least situation is $x \geq 10$ , and $- 3 x \geq 6$

Now, use the word ‘and’ and write the compound inequality then solve each inequality as follows:

$x \geq 10$ and $- 3 x \geq 6$

$x \geq 10$ and $- x \geq 2$

$x \geq 10$ and $x \leq - 2$

Since the intersection ‘and’ contains only the elements that belong to both sets, therefore the compound inequality is $x \geq 10$ and $x \leq - 2$ .

03

– Draw the graph for the compound inequality

The graph for the compound inequality is $x \geq 10$ and $x \leq - 2$ is shown below:

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

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