Question

Write a compound inequality to represent the sentences below.

a). A quantity x is either less than 10 OR greater than 20.
b) A quantity x is greater than 10 AND less than 20.

Answer 1

A quantity x is either less than 10 OR greater than 20 can be represented by the compound inequality x < 10 OR x > 20. A quantity x that is greater than 10 AND less than 20 can be represented as 10 < x < 20.

Step-by-step explanation:

To represent the compound inequalities based on the given sentences, we use inequality symbols to show the relationship between a quantity, x, and a set of values.

a) A quantity x is either less than 10 OR greater than 20.

The compound inequality for this statement is x < 10 OR x > 20. This means that the value of x is not between 10 and 20, but it lies outside this interval, on either side.

b) A quantity x is greater than 10 AND less than 20.

The compound inequality for this statement is 10 < x < 20. This indicates that x is strictly within the interval between 10 and 20, excluding the endpoints.