Post 5: What is Algebra?

Stumbling through corridors filled with numbers and symbols, Sage happens upon a glowing niche. Inside, a book. Sage reaches for the book and opens it. The title says it is “the book of the balancing of the equations”. Sage opens it and reads the first page.

“Do you want to help me play a game?” says a picture of a stern man. “Because playing this game will help you get out of here and back to reality.”

Ok, the man has Sage’s attention. Sage is ALWAYS up for a game, and going home is also high on his list right now.

The man points over Sage’s head and says, “Try to go through that door over there.” Sage turns and walks toward the door the man points to. A guard appears and stops him with his outstretched hand, demanding “What is x?” Sage looks at the walls around the door. It has many equations, some with “x”, but none of them tell him directly what “x” is. “You will not pass through this door until you tell me the correct answer” says the guard.

The man continues: “These equations. They are not useful in the forms that we see here: 2x+5 = 3x-6. They don’t tell me what I need to know. Sometimes, I can guess the useful form, but other times, I need to play THE GAME.”

Sage turns the page. Oh my, there is a bunch of math. The man continues: “Don’t despair. There are rules. You need to know them, and once you do, it won’t be scary anymore. Let’s get started with the first rule: An equation says that two things are equal. If they are equal, then when I do the same thing to both sides, they will still be equal. See this for yourself!” As Sage reads the words, a scratchpad appears:

Sage turns the page. The man looks at him - strange really, how a picture can look at the reader - and says “Have you convinced yourself? It is the first rule. Learn this rule well. When all other tricks fail you, you must come back and use this rule. Now see what it can do for us!”

“You see, we can move terms. We can use this to isolate x: when x+2+5 = 7, then x+2 = 7-5: There is now one term gone from the x-side. We can repeat this and get rid of the 2. Do you see how? 

• To move a term that was added, we subtract it on the other side.

• To move a term that was multiplied, we divide by it on the other side.

• Can you tell me the rules to get rid of terms that were subtracted or divided by? Hint: It’s just the other way around!”

“This is almost all we need to solve equations with one variable. But sometimes we will have more than one equation, with more than one variable. We call that a system of equations. Look at this example:”

"Remember this second rule: I can substitute things that are equal to reduce the number of variables. There are other rules, and many shortcuts, but if you forget all others, these two rules will be enough to solve most simple algebra equations. Remember them well!

When the gatekeeper asks you, don’t panic. Use the rules and play the game!”

Sage is psyched. He can play the game now! Bring it, gatekeeper! Uhh, what gatekeeper? Oh yeah. The rooms. Sage suddenly remembers reality. The black hole's edge is visibly closer to the room than it was previously. But Sage is no longer afraid - he has tools, and he is not afraid to use them.