When an inequality that has been graphed has a closed dot it could mean three things. These three things are that the inequality is equal to, greater than or equal to, or less than or equal to. When the dot is open, it means that it is greater than or less than, but never equal to. So if an inequality has an equal to sign, you know that it must always have an open dot instead of closed.
This week I am supposed to describe how to solve an equation such as 2X=16 in a way other than just dividing both sides by two. The way you can do this is by finding a common factor between the two numbers. In this case the common factor would be two. Then you have to see how many times the factor goes into the number on each side. In 2X=16, two goes into 2 once, and into 16 twice so you simplify the equation to X=8 which is in simplest terms. This method is called factoring. So you can kind of think of the problem as a big fraction and once you get X by itself, the problem is in its simplest terms and you are done. To me, this is not necessarily easier than just doing division, in fact they are pretty much the same. This is just another way to think of the problem.
I am algebra and there are many methods that we use to solve problems. Algebra is all about solving for X. In a normal equation with a variable on one side such as 3X+2=11, you have to do the opposite operation on both sides of the problem. So first you subract two from either side. The two cancels itself out and on the other side you end up with nine. So it would look like this: 3X=9. Then you have to divide both sides by three. The three cancels itself out and on the other side you get three, so X=3. This is a very simple solution, but is the pretty much where you start in algebra.
Did you know that there are an infinite amount of numbers between zero and one. This is beacause of the fact that decimals can go on forever and ever. Lets start out with the decimal .1. You can keep on adding more and more ones to that point one and you will never hit the number one. This can keep on going forever and you will srill never get to one. That is a very simple example of how there is a infinite amount of numbers between zero and one.
1/2= .5; 1/4= .25; 1/8=.125
These three equivalents show how the denominator of a fraction gets larger while the number gets smaller, but the question is why this happens. This happens because a fraction is basically just a different way to express a division problem. For example, 1/2 is the same as one divided by two. You are splitting one into two parts. Next, we have 1/4. This time you are splitting one into four parts and it equals .25. The same thing happens in 1/8. So the reason that the denominator of the fraction gets larger as the number gets smaller is because the larger the number you divide by, the smaller the answer will have to be. In my math class we just started a new topic but I'm not sure what it is because I missed that class today due to a dentist appointment. Anyways, last Friday we took our first test. This test covered positive and negative integers, order of operations, combining like terms, and the distributive property. The hardest part of this test for me, was the distributive property portion of the test. This topic is kind of confusing to me, but luckily I only missed one question on the test. I think that what we will start learning next will be more challenging, and I cannot decide whether or not I am excited about this, but I'm just glad I have a good teacher who obviously knows how to teach.
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