![]() ![]() Here I opened it becauseĦ4 was not a cool number. Not showing all the numbers in between- let'sĭrink exactly 64 ounces, so I'm going to fill And the way that I would beĭepict that on the number line- and obviously, I'm Loosen things a little bit? It's OK if I drinkĮxactly 64 ounces or more. So I'm not going to includeĦ4, but anything greater than that is completely cool. Strictly greater than, so in this situation it's not cool How would I depict that? Well, let me do my number I want to be bigger, so the opening is to the W. Think about, where I always want to drink more Should have at least- let me throw out a number- 64 Number of ounces of water I consume per day. Than and greater than or equal? Well, let's think aboutĪlso trying to increase the amount of water I intake. Other way around? What if you wanted to do greater OK, Sal, you did less than, you did less than or But then we show that, look, weĬan do everything below that. So we're only less than, we were very explicit that Notice, if we're includingġ,500, we fill in the circle. We want to make it very clear that we're not including On a number line is- let's say this is 0, this is 1,500, Is less than 1,500, the way we would depict that If it was just less than? So let me draw that, too. What about the situation where it wasn't less than or equal? What about the situation Less than or equal to 1,500 is legitimate. Than it, so then we would color in everything ![]() Look, we could be 1,500, so we'll put a little solidĬircle right over there. Than or equal to 1,500 a number line? Well, we would say, The way from 0 to 1,500, but let's imagine that Think about it, let's say that this right over Legitimate number of calories to have in a day. Over here, this is saying that C is less than Is to throw this little line under the less than sign. For more intricate graphs, you can also use inequalities with restrictions to shade selected parts of the graph. Use strict inequalities ( < and > < a n d >) for dotted lines and non-strict inequalities ( and a n d ) for a solid line.How could I express that? Well, the way I would do that With inequalities, you can add colored shading to your Desmos graph. So I can eat up to and including 1,500 calories? Right now, this is only up I can eat less than or equal to 1,500 calories, How can I express that? How can express that But what if I want to eat up toĪnd including 1,500 calories? I want to make sure that I But what about 1,500 calories? Is it true that 1,500 Or if I eat 1,400 calories, or if I eat 1,499 calories forĬ, those are all legitimate. I eat no calories in a day, or if I eat 100 calories, Keep in mind when I write that is obviously if Number of calories that I consume in a day Remember, the less than symbol, I make it point to Of calories in a day to be less than- and That as an inequality? Well, I want the number So, in particular, I want toĮat less than 1,500 calories in a day. To the number of calories I eat in a given day. Now that you have solved the inequality you might have "x " means it faces right and ""īit more care of my health, and I start counting There are exercises here on Khan for helping with that. You probably knew that but it's still important. ![]() We cant have any less than 7 tonnes because we are in business to make huge sums of money etc.Ī little practise will help you get there.The first step is to solve the inequality. If we go below that our operating costs might swamp the business - its just a made up story!įor the timber equation look vertically at the timber values, they are 1/2 and 1 so we getġ/2x + 1y is greater or equal to 7 (from the statement below the equations again). We cant have any less than 10 tonnes because we are in business to make huge sums of money. The maintenance crew has told management that the trains cannot make any more than 8 trips per day (each train)įor the coal equation look vertically at the coal values, they are 2 and 1 so we getĢx + 1y is greater or equal to 10 (from the statement below the equations). Train B can carry 1 Tonne of coal and 1 Tonnes of timber per trip.Įach day the trains need to deliver at least 10 Tonnes of coal and 7 Tonnes of timber. Train A can carry 2 Tonnes of coal and 1/2 Tonne of timber per trip. Notice that they look like a set of simultaneous equations the way they are written. And by the way, the two graph lines above are not considered difficult enough for the standard. ![]()
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