New week, and a wonderful new schedule! First up, Algebra II!

Today, I covered Inequalities, and systems of inequalities. Let’s start with basic inequalities, and the trichotomy property. This is also known as the property of order. It is vital for the rest of the properties of inequality, and can be summarized as follows:

- For any two real numbers, A and B, one of the following statements is true:
- A < B
- A = B
- A > B

Now, onto the properties of inequality

- Addition and Subtraction Properties of Inequality
- For any real numbers A, B, and C
- If A > B, then A +/- C > B +/- C
- If A < B, then A +/- C < B +/- C
- Also true for <= and >=

- For any real numbers A, B, and C
- Multiplication and Division Properties of Inequality
- For any real numbers A, B, and C
- If A > B, then A */÷ C > B */÷ C
- If A < B, then A */÷ C < B */÷ C
- CORRECTION: If C is negative, than you invert the < or >. If A > B, then A * -C < B * -C
- Also true for <= and >

- For any real numbers A, B, and C

And then, there are two kinds of compound inequalities. “And” inequalities, & “Or” inequalities.

- And: A < B < C
- B is greater than A
**AND**less than C. - EXAMPLE: 5 < B < 7
- On a number line, all solutions lie between two points.

- B is greater than A
- Or: B < A OR > C
- B is less than A,
**OR**it is greater than C - EXAMPLE: B < 5, or B > 7
- On a number line, no solutions lie between two points.

- B is less than A,

Absolute value inequality systems are where it gets complicated. Absolute value is the distance from zero on a number line, so how does that factor into inequalities?

Take this equation:

|A| < 4

What this means, is that A must be less than 4 away from zero in both directions. In this case, every solution is between positive and negative 4.

They can also be represented like this:

|A| < 4 = -4 < A < 4

However, it is different if you are saying that |A| is greater than a number. In that case, it means that A must be, for example, 4 spaces away from zero, resembling an OR inequality more.

After that giant wall of text, I did more reading of the wonderful Don Quixote.

First of the chapters: Don Quixote mentions that his helmet is damaged, and he will take a helmet from the next fellow knight he sees. Sancho, his squire, mentions that he probably won’t see another knight. Ever. And that he should really get his wounded ear looked at. Don Quixote just says that there exists a potion which will cure it in 1 drop. But he doesn’t have any.

Second of the chapters: Don Quixote meets some goatherds that invite him to eat dinner with them. He agrees, and recites some of his madness that they mistake to be ultimately profound. One of them bandages his ear properly and puts medicine on it.

Third of the chapters: Don Quixote hears about the upcoming burial of a man that lived strangely in his final days, and hears a story that can be boiled down to this: “That girl is beautiful! And… she’s a shepherd. EVERYONE, PUT ON SHEPHERD ROBES AND FOLLOW HER AROUND!” Don Quixote decides to go to the funeral.

Lastly, Marine Biology. Two big things, spacial distribution (habitats) and reproduction/evolution.

As habitats are easy to explain (it’s where life lives, yo) I’ll move straight onto the section on reproduction and evolution. Please have your parents and pastor approve you reading this next section.

Did you get their approval? Yes? Good.

Now, the root of evolution is mutation from reproduction. Small changes in genetic material can make an organism more fit to survive in it’s environment and face challenges. This also works in reverse. A deer with bright pink fur will not survive for long, sticking out like a sore thumb to any predators. And hunters. However, some can be helpful. Like a deer that is born with the ability to turn invisible. Not all mutations are passed down through generations, as an invisible deer might be very hard to find and mate with. Or it could starve to death before it reproduces.

Now, there are 2 main types of reproduction. Sexual and Asexual reproduction. Sexual reproduction takes more than 1 organism, and Asexual reproduction is a solo effort.

However, I’m getting ahead of myself. Reproduction can be defined as follows: An organism replaces itself with an offspring capable of reproducing (by the same definition).

You might be thinking, “wait, if reproduction is just replacing the parent, why am I not exactly like my parents?”

Well, there’s an answer! Humans use sexual reproduction, meaning that each parent contributes only half of their genetic material to the child. In this case, 23 chromosome pairs per parent.

So while you might have gotten that weird birthmark from your mother, you have also got that premature baldness from your father. Have fun!