Start with a graph and write the inequality from the graph.
Inequality: x< 0 OR x> 100 Graph:
Practice makes perfect
We are told that water is not a liquid when its temperature is above 100^(∘)C or below 0^(∘)C. Let's break down what this means, graph it, then write a compound inequality to represent the solution set.
Graphing the Compound Inequality
The first thing to notice about the given information is the key word or. This tells us that we have an or inequality, whose solution set is the region to the left of the lesser value 0^(∘)C and the region to the right of the greater value 100^(∘)C.
Finally, the words "above" and "below" tell us that neither the lesser value nor the greater value is included in the solution set, which is shown with open circles on the number line.
Forming the Compound Inequality
Consider the lesser point, 0^(∘)C. The solution set we showed in the graph lies at the left of this point, and the circle at this point is open. This means that water is not liquid at any temperature less than 0^(∘)C.
x < 0
The solution set also lies at the right of the greater point, 100^(∘)C, and this point is also open. This means that water is not liquid at any temperature greater than 100^(∘)C.
x > 100
These two statements form an " or" compound inequality.
x < 0 OR x > 100
