Question

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

Short answer

The compound inequality whose graph is empty set is $x\ge 10$and $-3x\ge 6$.

Step-by-step solution

– Define the inequalities 

Let a variable $x$.

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

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

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

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

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

$x\ge 10$and $-x\ge 2$

$x\ge 10$and $x\le -2$

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

– Draw the graph for the compound inequality

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

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