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Solving and Graphing Inequalities using Addition or Subtraction - Problem 1
To solve and graph the solution to a word problem using an inequality, first write out an inequality statement. Remember that "at least" means "greater than of equal to", and that "no more than" means "less than or equal to". When graphing, draw and label a number line. If the inequality is "equal to" a number, put a closed circle above that number. If the inequality is "greater than" or "less than" but not "equal to", then put an open circle above that number. Use an arrow to indicate all the values that fall within the inequality -- "greater than" or "greater than or equal to" means the arrow will indicate all the values above the number (to the right); "less than" or "less than or equal to" means the arrow will indicate all the values below the number (to the left).
For a lot of students word problems can be really intimidating but don't worry about it. I promise sometimes they can be even easy. Let's look at this one and see if we can figure it out. Write the following as an inequality and graph the solution. You must buy at least three phone numbers to get a discount on the phone plan.
Before you do any writing think about what that means. It's like you go in and you want to set up a new phone plan for you and your family or whatever and you need to activate at least three numbers. That means you can activate three numbers or 4 or 5 or 6 or 7 or whatever or 10. It could be any number you want to but it has to be three or bigger.
So here's how you would write this using words: number you buy or number you activate has to be bigger than or equal to 3, we can write at least 3 as greater than or equals to 3. I'm just going to pick to represent that as a variable. I'm going to use the letter x, I just picked that. You can use p, you can use m, you could use any letter you want to. But this inequality statement shows that you need to buy three or more phone plans, or phone lines in order to get the discount.
Let's go ahead and graph it on a number line. You need to make sure 3 shows up on there and then since I have this inequality symbol that uses greater than or equal to, that means I'm going to have a closed circle at 3 and then I want the arrow to mark anything that's bigger than 3. This arrow goes out towards infinity. I could buy 3 plans or 4 plans or 5 plans or 10 plans or 100 plans, any number that's greater or equal to 3 is a solution to the inequality that I wrote.
So you guys when you see word problems you can do it. Like this one took us about 30 seconds and only about three lines of writing so you can do it. Don't just give up and don't skip those homework problems. Just spend a little time. If it helps you translate it into words, do that first.