Equations

Equations

What is an equation?

An equation is a type of exercise that carries a == sign which, on each side of the sign, that is, in each member of the equation there is an algebraic expression.


An algebraic expression can be anything -> just a number, just an unknown or well, an exercise with number and unknown.

  • In an equation the unknown can appear several times
  • In an equation several unknowns can appear

Types of Equations

First-degree equation -> It is an equation whose unknown is raised to the first power.
Quadratic equation –> It is an equation whose unknown is squared, that is, raised to the second power.

Clue to Solve an Equation

Perform several mathematical operations on both sides of the equation at the same time to isolate the variable (leave it alone on one side of the equals sign) and solve for it.
The equation will be solved once you manage to arrive at a true statement.

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?

What is an equation?

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×+2=104 \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 1010.
In these cases, you wondered: what plus 22 equals 1010? The number 88!
44 times what equals 88? The number 22! 22 is the number that will appear in the box.

Indeed, 22 was an unknown -> an unknown that you have discovered. By substituting 22 in the box we actually got 1010.
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 XX and the second is YY.

An equation is symbolized with the sign ==
which means that a certain expression is equivalent to something
Let's place XX in place of the previous box.
We will obtain:
4×X+2=104 \times X+2=10
This is an equation!

What do you say? Is this an equation?
1+X=21+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=42X=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+X2+5X=10+X
This equation tells us that the entire expression on the right is equivalent to the entire expression on the left.
The XX on the left is exactly the same as the XX 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=22=2
1=11=1
4=44-=4-
A false statement, on the other hand, is never true, such as:
2=32=3
4=94=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=5X+2=5
If we place X=3 X=3 
We will obtain:
3+2=53+2=5
5=55=5
True statement!
On the other hand, if we place any other number, like X=4X=4 we will arrive at a false statement and, therefore, it will not be the solution to the equation.


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Types of Equations

First-Degree Equations

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×X=80X5 \times X=\frac{80}{X}

Quadratic Equations

Second-degree or quadratic equations are equations whose unknown is raised to the square.
For example:
X2+3x+4=X^2+3x+4=


Clue to Solving Equations

To solve the equation we will perform several mathematical operations on the 22 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 4+X=6
We will want to isolate the variable XX on a single side of the equation, therefore, we must subtract 44.
We will subtract 44 from both sides of the equation.
This means that we will obtain:
X=64X=6-4
X=2X=2
We have solved the equation!


Another example:
Solve the equation
4X=124X=12
We want to isolate the variable XX, therefore, we will divide the entire equation by 44.
We will obtain:
X=12:4X=12:4
X=3X=3
We have solved the equation!