Question

How do you solve the linear equation $4x - 15 = 6x - 1$?

Answer 1

Hint: Given a linear equation in one variable which is varying in $x$. We know that the standard form of linear equation in one variable is given by $ax + b = 0$, where the value of the coefficient of the $x$ term is not equal to zero. That is $a \ne 0$, $b$ may or may not be zero. Here we find the solution of the equation by rearranging the like terms together.

Complete step-by-step solution:
Considering the given linear equation $4x - 15 = 6x - 1$ below:
$ \Rightarrow 4x - 15 = 6x - 1$
Now converting the above given linear equation in one variable into the standard form of the linear equation in one variable, as shown below:
By transferring the like terms and the unlike terms on one side of the above equation, as shown below:
$ \Rightarrow 4x - 6x - 15 + 1 = 0$
Now simplifying the above equation as shown below:
$ \Rightarrow - 2x - 14 = 0$
Now multiplying the above equation with -1 as shown below:
$ \Rightarrow 2x + 14 = 0$
Now moving the constant to the other side of the above equation as shown below:
$ \Rightarrow 2x = - 14$
Now dividing the above equation by 2, as shown below:
$\therefore x = - 7$
So the solution of the variable $x$ is equal to -7.
The solution of the given linear equation in one variable $4x - 15 = 6x - 1$is equal to -7.

Note: Please note that instead of grouping like terms and the unlike terms together we can actually group all the terms on one side of the linear equation which is the similar form of the standard linear equation $ax + b = 0$, and then divide the equation with $a$, and then moving the constant to the other side which brings the solution to $x = \dfrac{{ - b}}{a}$.