Algebra

Algebra is simple. It just use alphabets to replace numbers. But the use of algebra is very useful.

The Concept of Algebra

Algebra is just simple, right? Using alphabets to convert it into numbers. You can even make equations from it. For example, if there are 3 planets in the TOI-700 system, and 5 more in the Solar System…

You get… 8! In fact, you are using this to quickly think of the ways to calculate that. The equation is x-3=5, so you come up with 3+5. That’s not a big deal for simple works but it is vital for more complex things.

For example, coincidentally, every rocky planet has 2 moons and each gas giant has 5. You get 7 planets and 20 moons. How many gas giants are there? The solution is:

k=rocky planets; y= gas giants
2k+5y=20
k+y=7
2k+2y=14
3y=6
y=2
There are 2 gas giants in the system.

How to Solve Equations

If you get stuck, you can read the section here.

To solve an equation, not much effort needs to be paid if you understand how it works. First of all, you have to turn the number into the unknown on one side and do the same thing on the other but not turning it into 0. For example:

a-88=92
a-88+88=92+88 (the action is to make the value of the side of a exactly a.)
a=190

b*4=20
b*4/4=20/4 (the action is to make the value of the side of b exactly b.)
b=5

Then, for equations with multiple unknowns, you need to get this: You need to make the 2 sides with the same unknown equal, and figure out the difference and the unknowns. Remember the rocky planets and gas giants’ example? It is one that uses this method to solve.

For even more difficult ones that cannot be solved with these concepts, we need to figure out that: If we need to move the number or unknown to the other side, the operation needs to be the opposite. This is an easy example.

y+2=5
y=5-2 (doing the opposite operation on the other side)
y=3

Oh, by the way, it is the first method mentioned before, being even simplified.

Algebra in indexes

I talked about there are other uses of algebra. For example, indexes, which are about exponentiation, uses it. We know when x^2 * x^3, we’ll get x^5. But in this case, except only representing the unknown, we can also use algebra to solve some problems about simplifying.

Going Farther and How to Think

Algebra’s use is way broader than you can even imagine. From simple maths, to complicated ones including calculating the gravitational pull of planets to point out a missing planet, or when figuring out how to correct the trajectory of a probe.

Learning about algebra and how to use it is good for you. We can then put the unknown in an equation and solve it. To get the concept by yourself, you can figure it out by simple logic and calculate it with the integer representing the alphabet. For example, to proof the solution of a+3=8, you only need to use 5+3=8 to prove it.