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Solving and Graphing Inequalities using Multiplication or Division - Problem 3

Teacher/Instructor Alissa Fong
Alissa Fong

MA, Stanford University
Teaching in the San Francisco Bay Area

Alissa is currently a teacher in the San Francisco Bay Area and Brightstorm users love her clear, concise explanations of tough concepts

To solve and graph the solution to a word problem using an inequality, first write out an inequality statement based on the information in the problem. Remember that "at least" means "greater than of equal to", and that "no more than" means "less than or equal to". Solve the inequality by using inverse operations. Remember to change the inequality sign if you multiply or divide both sides by a negative value. When graphing the inequality on a number line, keep in mind when to use an open circle versus a closed circle, and which direction the arrow should be pointing.

One of the things I'm sure you guys have experience with is cell phones and how to deal with text messaging, how much you pay for your cell phone all that kind of stuff. So this is what's happening in my text situation. You have $15 to spend on text messages, in your phone plan each text costs 20 cents. Write an inequality to show how many texts you can send.

So like for me personally when I was trying to figure out if I should like pay a certain amount and have like unlimited texting or else pay for each text, this is what I was thinking about. You guys Math really does help in the real world and this is a situation where it might help you.

So if I wanted to spend $15 but that's it on text messaging, I'm going to have to use this information. Before we do that also you guys probably know that you also pay when you receive texts so this doesn't account for receiving texts. This is only for sending.

Okay I have $15 to spend on text messages that means however much I spend has to be lea than equal to 15 whatever I spend. I'm not sure what goes there yet but whatever I spend has to be less than or equal 15. Okay each text costs 20 cents so I'm going to write .20x where x is the number of texts that I could send.

Okay so now let's go ahead and solve it. I know .20x is less than or equal 15 in order to get x all by itself I'm going to divide both sides by .20 and I get that x is less than or equal to 75. What that means is that I could text I could send out 75 or fewer texts and not exceed my $15 limit.

So when you're going to buy a cell phone this is the kind of math you're going to want to think about. Like is it more cost effective for me to pay the lump sum and to just have unlimited texting or do I want to just restrain myself and just pay 20 cents per texts. Let's figure out how many I could send per month.

It's totally up to you but you guys you can use these inequalities in the real world. You don't have to carry around your calculator and you're like dorky Math, you know book or whatever. You can just do this in your head if possible but inequalities are a really great tool to use anytime you're shopping or spending something or comparing different options, which one's better? What's the maximum I could spend for my $15, maximum I could text for my $15 or whatever. So again this is a word problem that wasn't too bad. I promise you guys you can do the word problems if you try them.

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