# How to solve an equation in math?

Before **solving an equation** , you need to understand the definition and meaning of this word that is part of **the mathematical vocabulary** .

An equation is an equality consisting of a variable, usually called *x,* that is used to solve problems.

During primary education, they learn **the basis of mathematics** , such as addition, subtraction, multiplication or even mental math.

In general, it is in 1st year of ESO when math exercises consist of equations, which normally appear in this form:

*7x + 5 = 3x – 15*

It is then that the student discovers the famous unknown *(x)* and when he will have to learn to solve an equation .

From 2nd ESO the equations are complicated to increase the level of the students, which will be more demanding in the 2nd Cycle of Secondary Education (3rd and 4th ESO).

Throughout ESO and up to higher education, for those who decide to continue in the **scientific branch such** as the Baccalaureate of Sciences, the equations will never disappear.

Therefore, it is necessary to learn to solve them!

**First degree equations** are the first to be learned and are considered the easiest to solve.

The method to adopt is the following:

*isolate unknown**x*- regroup the terms
- divide (or subtract, multiply, according to the equation)
*deduce the solution, called**S*

For example, for the equation 3 *x* -5 = – *x* +2, **the calculation** should look like this:

3 *x* + *x* = 5 + 2

4 *x* = 7

*x* = 7/4

Therefore, S = 7/4 = 1.75

When **the method for an equation** of the first degree is already assimilated, you can learn to solve a **quadratic** or **second degree ****equation** : (a *x* + b) (c *x* + d) = 0.

The basic rule that your **math teacher** will repeat is that *if the product of two numbers is 0, then at least one of the factors is 0.* From then on, you will have to solve as many equations as there are factors in the statement.

But, there are other **systems of equations such** as the case of rational equations that can be more complicated, according to many students.

A **rational equation** is presented in this form: f ( *x* ) / g ( *x* ) = 0.

You have to know **the ****theorems** when you want to solve these types of equations, that is, *a quotient is 0, if at least its numerator is 0 and its denominator is not.*

The process can look like this equation, in which you have to use the products of x:

*x* / *x* +1 = *x* -1 / *x* +2

*x* ( *x* +2) = ( *x* −1)

( *x* +1) x ( *x* +2) – ( *x* −1) ( *x* +1) = 0

*x* ² + 2 *x* – ( *x* ² – 1) = 0

*x* ² + 2 *x* –x² + 1 = 0 2

*x* + 1 = 0 *x* = – (1/2)

Therefore, the solution is S = – (1/2).

Sometimes, it is also about **expressing a mathematical problem through an equation** , and this same one in geometry.

In this case, it’s about using **the problem-solving methodology** while adding everything you know about the equations.

Specifically, you have to **translate the sentence into mathematical writing** and then solve the necessary equations.

Do not forget to write the solution literally. How to solve an equation in math?