Example of Solution of Equations

In the translation from ordinary language to symbolic language, we have seen that the approach frequently leads us to expressions in which the symbol of equality is included. We define these expressions in the topic of Unit III with the name of equations; we said that an equation is a conditional equality for certain values ​​of the variable. Finding those values ​​that form the solution set is the process of solving the equation or as it is also called, the process of solving the variable or unknown.

As we will remember, the process of solving an equation or solving an unknown consists of going step by step transforming the equation given in another equivalent, using the properties of Equality, postulates and theorems already proven.

EXAMPLES OF SOLUTION OF EQUATIONS:

4x + 6 = 2x + 18⇒2x + 6 = 18

(We add -2x to each side of the equality)

With the same additive property of equality we can transform the expression

2x + 6 = 18⇒4x + 6 = 2x + 18

(We add 2x to each side of the equality)

That is, we can use the double implication

4x + 6 = 2x + 18⇔2x + 6 = 18

so both expressions are equivalent or mean the same and therefore we can be sure that they have the same solution set for X.

2x + 6 = 18⇔ 2x = 12 (Adding-6)

2x = 12 ⇔ x = 6 (Multiplicative Property1 / 2 and Division Theorem) 

therefore 4x + 6 = 2x + 18 ⇔ x = 6

Verification:

4(6) + 6= 2(6) + 18

24 + 6 = 12 + 18

30= 3