Inequalities and Their Graphs – Practice Problems

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Different from equations, inequalities tell us that two values are not equal, but something else. A value can be more than or less than, more than and equal to or less than and equal to.

How do you know which is which? Pay attention the direction of the inequality symbol, it always points to the value that is less than and keep an eye out for a line under the more than or less than symbol, that tells us the value can also be equal to.

Graphing inequalities on a number line is very helpful to visualize the solution set. If a number is greater than 5, write an open dot on the number 5 and draw a line from the open dot to include all the number greater than 5. The open dot indicates the number 5 is not included in the solution set. If a closed dot is used, the number indicated is included in the solution set.

Why do we learn about inequalities? Of course, we need to know about this topic to get a good grade in math but also for real world use. A speed limit of 55 mph means you must drive less than or equal to 55 mph. Watch this video to find out what happens when Timmy drives too fast.

Use inequalities to solve problems. CCSS.MATH.CONTENT.HSA.CED.A.3

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Exercises in this Practice Problem
Describe the process of graphing inequalities.
Explain the meaning of the graphs.
Determine all speeds that will not result in a speeding ticket.
Match the correct inequality with the graph.
Translate the words into a mathematical sentence using inequality signs.
Describe each situation using inequalities.