Question

Which set of numbers is included as part of the solution set of the compound inequality x < 6 or x > 10? {–7, –1.7, 6.1, 10} {–3, 4.5, 13.6, 19} {0, 6, 9.8, 14} {8.5, 9.1}

Answer 1

The correct set of numbers that are part of the solution set for the compound inequality x < 6 or x > 10 is {-3, 4.5, 13.6, 19}, as all these numbers satisfy at least one part of the inequality.

Step-by-step explanation:

The compound inequality x < 6 or x > 10 indicates two separate conditions, where either one can be true for a number to be part of the solution set.

Looking at the question, we need to find which set of numbers falls either below 6 or above 10.

Let's evaluate the provided sets:

1. {–7, –1.7, 6.1, 10} – Only –7 and –1.7 meet the inequality conditions.
2. {–3, 4.5, 13.6, 19} – All of these numbers satisfy at least one part of the inequality: –3 and 4.5 are less than 6; 13.6 and 19 are greater than 10.
3. {0, 6, 9.8, 14} – 0 is less than 6, and 14 is greater than 10. However, 6 and 9.8 do not meet either condition.
4. {8.5, 9.1} - Neither of these numbers meet the conditions as they are between 6 and 10.

Therefore, the set that is included as part of the solution set of the compound inequality x < 6 or x > 10 is {–3, 4.5, 13.6, 19}.