Question

Solve $2x - 5 = 3\left( {x - 5} \right)$ for the value of $x$

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 2x - 5 = 3\left( {x - 5} \right)$
Expanding the right hand side of the above equation as given below:
$ \Rightarrow 2x - 5 = 3\left( {x - 5} \right)$
The right hand side of the above expression is expanded and multiplied the number 3 with $x - 5$, which gives the product of 3 and $x$ minus the product of the number 3 with the number 5, which is as given below:
$ \Rightarrow 2x - 5 = 3(x) - 3(5)$
So the right hand side of the given equation is the difference of the multiplication of the number 3 with $x$ and the multiplication of the number 3 with the number 5.
Which gives the multiplication of the number 3 with $x$, gives the result of $3x$, whereas the multiplication of the number 3 with the number 5, gives the result of 15.
Hence the simplification of the right hand side gives the difference of $3x$ and 15, which is as given below:
$ \Rightarrow 2x - 5 = 3(x) - 3(5)$
$ \Rightarrow 2x - 5 = 3x - 15$
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.
$ \Rightarrow - 5 + 15 = 3x - 2x$
$ \Rightarrow 10 = x$
Here the consonant -15 is grouped with -5 on the other side, where $2x$ is grouped with $3x$ on the other side as shown in the above expression.
$\therefore x = 10$

The value of $x$ is 10.

Note: 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 $x$.