Question

How do you solve $6x - 3 = 8x - 9$?

Answer 1

This problem deals with solving the linear equation with one variable. A linear equation is an equation of a straight line, written in one variable. The only power of the variable is 1. Linear equations in one variable may take the form of $ax + b = 0$, and are usually solved for the variable $x$ using basic algebraic operations.

Complete step-by-step answer:
Given a linear equation one variable which is considered as given below:
$\Rightarrow 6x - 3 = 8x - 9$
Now rearrange the terms such that all the constants are on one side of an equation and all the $x$terms are on the other side of the equation.
Now moving the term $8x$, which is on the right hand side of the equation to the left hand side of the equation, as shown below:
$\Rightarrow 6x - 3 - 8x = - 9$
Now on the left hand side of the equation the number -3 is moved to the right hand side of the equation, as shown below:
$\Rightarrow 6x - 8x = - 9 + 3$
Now simplifying the above equation, as the like terms are and the constants are grouped together.
Taking the term $x$ common on the left hand side of the above equation, as shown below:
$\Rightarrow \left( {6 - 8} \right)x = - 6$
$\Rightarrow - 2x = - 6$
Now multiplying the above equation with -1, so as to remove the negative sign on both sides of the equation, as shown below:
$\therefore x = 3$

The value of $x$ is 3.

Note:
Please note that the linear equations in one variable which are expressed in the form of $ax + b = 0$, have only one solution. Where a and b are two integers, and x is a variable. This means that there will be no terms involving higher powers of x, not even the power of 2, which is ${x^2}$.