Question

How do you solve $4x - 2 = x + 7$?

Answer 1

Hint: First of all this is a very simple and a very easy problem, this problem deals with simple and basic algebraic mathematics. To solve this problem one should be familiar with the basic concepts in the algebra, such as simplifying the given expression or an equation which is in an algebraic expression. Given an algebraic expression we should be able to do all kinds of algebraic calculations.

Complete step-by-step solution:
Given that the equation as given below:
$ \Rightarrow $$4x - 2 = x + 7$
Now the above obtained equation is arranged in such a way that all the like terms are the unlike terms are grouped together, here the like terms are meant by the terms that have the same variable terms are grouped together and the terms which are constants are grouped on the other side. Now the like terms which are grouped together on one side, where the consonants are grouped together on the other side.
Take multiple of x in left hand side of the above equation as mentioned below:
$ \Rightarrow $$4x - x = 2 + 7$
The left-hand side of the above expression having multiple of x and right-hand side have constant value.
$ \Rightarrow $$3x = 9$
Divide right-hand side of the expression with the number 3, which is multiple of x.
$ \Rightarrow $$x = \dfrac{9}{3}$
Here the numerator is 9 and the denominator is 3. Where 9 is a multiple of 3. So, when we divide numerator by denominator, we will get an integer value-
$ \Rightarrow $$x = 3$

Therefore, the value of x is 3.

Note: Always remember that the Constants are those terms which are fixed numbers, and do not change if the variable changes. Whereas the variable terms are those terms where the fixed numbers or consonants are multiplied with a variable like x, then these fixed terms also change due to the presence of the variable x, according to the change in the variable x.