Equations

In this article, you will learn for the first time what equations are, you will know the different types, and maybe you can even solve some! Shall we start?

So far, in elementary school, you have solved equations without realizing that you were doing it.
Do you remember exercises that looked more or less like this?
$4 \times ⬜+2=10$

In this type of exercises, you had to figure out what number should appear in the box for the result to actually be $10$.
In these cases, you wondered: what plus $2$ equals $10$? The number $8$!
$4$ times what equals $8$? The number $2$! $2$ is the number that will appear in the box.

Indeed, $2$ was an unknown -> an unknown that you have discovered. By substituting $2$ in the box we actually got $10$.
From now on, we no longer use the box and move on to denote unknowns with letters.
The most common letter for denoting unknowns is $X$ and the second is $Y$.

An equation is symbolized with the sign $=$
which means that a certain expression is equivalent to something
Let's place $X$ in place of the previous box.
We will obtain:
$4 \times X+2=10$
This is an equation!

What do you say? Is this an equation?
$1+X=2$
The answer is of course!
We have here something that equals something else. Indeed, with a variable that we must find.
And this? Is it an equation?
$2X=4$
Of course! It's an equation no matter how you look at it!
One side equals another side.

In equations, the unknown can appear more than once, in different ways, as seen in the following equation example:
$2+5X=10+X$
This equation tells us that the entire expression on the right is equivalent to the entire expression on the left.
The $X$ on the left is exactly the same as the $X$ on the right.

In general terms, an equation is a type of exercise that carries a sign $=$ that, on each side of the sign there is an algebraic expression.
An algebraic expression can be anything: just a number, just an unknown, or an exercise with both number and unknown.

To know how to solve equations you must be familiar with expressions such as true statement and false statement.
A true statement is an equation that is always true.

As in the following example:
$2=2$
$1=1$
$4-=4-$
A false statement, on the other hand, is never true, such as:
$2=3$
$4=9$

When solving an equation, we try to find the number or numbers that, by placing them in place of the unknown, we arrive at a true statement.

For example, in the equation:
$X+2=5$
If we place $X=3$
We will obtain:
$3+2=5$
$5=5$
True statement!
On the other hand, if we place any other number, like $X=4$ we will arrive at a false statement and, therefore, it will not be the solution to the equation.

First-degree equations are the simplest equations, appearing with a single unknown raised to the first power.
The unknown can appear as a fraction or as a factor.
For example:

$5 \times X=\frac{80}{X}$

Second-degree or quadratic equations are equations whose unknown is raised to the square.
For example:
$X^2+3x+4=$

To solve the equation we will perform several mathematical operations on the $2$ sides of the equation at the same time to isolate the variable, leaving it alone on one side.
For example:
In the equation
$4+X=6$
We will want to isolate the variable $X$ on a single side of the equation, therefore, we must subtract $4$.
We will subtract $4$ from both sides of the equation.
This means that we will obtain:
$X=6-4$
$X=2$
We have solved the equation!

Another example:
Solve the equation
$4X=12$
We want to isolate the variable $X$, therefore, we will divide the entire equation by $4$.
We will obtain:
$X=12:4$
$X=3$
We have solved the equation!