Review the assigned reading to prepare for this discussion.
Linear inequalities come in one of the following basic forms:
a < x < b
x < b
x > a
x < a or x > b
Note: The < (less than) can be replaced with (equal to or less than), and > (greater than) can be replaced with (equal to or less than) in any of these cases, depending on the context of the problem or situation.
On a daily basis, you are likely to come across situations in which inequalities are alluded to (e.g. less than, more, at least, or between) without realizing the connection to math.
Example:
Perhaps you ordered furniture from a local department store and were given a delivery time window between 10 am and 2 pm on a certain day. This situation can be modeled using one of the four inequalities listed above. Additionally, the situation can be modeled graphically and with interval notation, as shown below.
Description: The furniture I ordered will be delivered between 10 am and 2 pm.
Inequality: 10am x 2pm
Interval notation: [10:00am, 2:00pm]
Graph:
Inequality Graph with inequality 10am x 2pm and interval notation 10:00am, 2:00pm
Respond
Come up with a real-life situation that models each of the four types of inequalities listed above.
Provide a written description of the situation.
Express the situation using the appropriate inequality and the correct units (time, money, weight, etc), if applicable.
Express the situation using interval notation.
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