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Solving and Graphing Inequalities using Addition or Subtraction - Problem 3
To solve and graph the solution to a word problem using an inequality, first write out an inequality statement. Solve the inequality using the same rules that apply to solving an equation. In other words, use inverse operations to "undo" what is being done to the variable. When graphing the inequality, keep in mind when to use an open circle versus a closed circle, and which direction the arrow should be pointing. Lastly, make sure you solution makes sense. For example, if the answer is referring to how much money you spent, you cannot spend a negative amount of money, when you graph, make sure the arrow stops at 0 and does not go into the negative side of the number line.
This is another word problem that's involving inequalities and the way I know that is because the word ‘inequalities’ shows up in the problem. You get $20 per week for allowance. You already spent $3.18 for online music. Write and solve an inequality to describe how much you can spend in the rest of the week.
Okay so we've got to figure out how to write an inequality meaning it's going to use one of these signs, one of those symbols to describe this situation. Alright, you start with $20, we know that then what happens? Then you spend $3.18 so since you spent it, I'm going to subtract $3.18. That's what happened and then you have some amount left. I'm going to call that amount x.
So when it comes to how much money you can spend, we're going to have to fill in this blank with some kind of inequality symbol. First let's go ahead and do 20 take away $3.18. It's going to be $16.82. That's how much money you have left in your pocket. You can spend that much or you might spend less than that. So the amount you can spend might be equal to that amount or you might choose to spend less and like keep some for next week or whatever.
So when you're asked to write an inequality you could say $16.82 is greater than or equal to how much I have left to spend. I might only spend $10, I might only spend $12, any number I pick has to be less than $16.82.
So there's my inequality. Let's go ahead and graph it and the graph is neat because it shows how much money I have that I can put out of my pocket. I'm going to say $16.82 is somewhere between 16 and 17. I'm just going to approximate here and you'll have to ask your teacher how precise he or she wants you to be. There's my dot that represents $16.82 and my x number needs to be less than that, so I'm going to draw an arrow in this direction. Wait, wait a second though. In my picture there I just went beyond zero so it's like I'm spending negative money, but you can't spend negative money right guys? You can't, like that doesn't make sense, negative money. So I'm just going to stop my graph right there. In fact I'm going to put a closed circle on zero and you may or may not know what that means yet but I'm just going to tell you like it makes sense in the real world. We can't spend negative money. You can't have any solutions that are negative values. That's why this problem has this kind of funny dumbbell shape and you'll get into that more when you start looking at compound inequalities.
Before I let you guys go I just want to remind you that word problems look scary. A lot of students skip them right away but you can be like the A+ kid who does his homework and who shows up and says I know that problem. I can share it and maybe you can do it on the board and get extra credit or something. These word problems are not so bad you guys. You can do them, just slow down, try to figure out what's going on, take it step by step and I bet you're going to be really successful.