Question

How do you solve $2x - 4 = - 4x - 4 + 6x$?

Answer 1

Hint: In this question, we want to solve the linear equation of one variable. A linear equation of one variable can be written in the form $ax + b = c$. Here, a, b, and c are constants. And the exponent on the variable of the linear equation is always 1. To solve the linear equation, we have to remember that addition and subtraction are the inverse operations of each other. For example, if we have a number that is being added that we need to move to the other side of the equation, then we would subtract it from both sides of that equation.

Complete step-by-step answer:
In this question, we want to solve the linear equation of one variable.
The given equation is,
$ \Rightarrow 2x - 4 = - 4x - 4 + 6x$
Let us solve this equation,
First, we will add -4x and 6x on the right-hand side.
That is equal to,
$ \Rightarrow 2x - 4 = 2x - 4$
Here, we have a number 4 that is being subtracted and we need to move to the right-hand side, we will add it from both sides.
Now, let us add 4 on both sides.
$ \Rightarrow 2x - 4 + 4 = 2x - 4 + 4$
That is equal to,
$ \Rightarrow 2x = 2x$
Here, we have a number 2 that is being multiplied and we need to move to the right-hand side, we will divide it from both sides.
Now, let us divide by 2 into both sides.
$ \Rightarrow \dfrac{{2x}}{2} = \dfrac{{2x}}{2}$
So, the answer is
$ \Rightarrow x = x$
A solution to this means that ‘x’ can take on any value and still satisfy the original equation.

Note:
When we get one variable equation such as x=x, where both sides of the equation are the same, this is a clue that ‘x’ can take on any value because both sides of the question will always simplify to the same answer respectively.