Question

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

Answer 1

Hint: In this question, we have been given a linear equation in one variable which we need to solve to find the value of \[x\]. Also, it's important to realize that there are multiple ways to solve problems like these.

Complete step-by-step solution:
First, look for any like terms we can combine. On the right-hand side, we have a \[ - 4x\] and a \[6x\] .
We can add these to get \[2x\] .
So, the new equation we will get after performing this operation will be as shown:
\[2x - 4 = 2x - 4\] …. (1)
Notice both sides of the equation (1) are exactly the same.
We can add 4 to both sides, which will cancel out both and leave us with
\[2x = 2x\] …. (2)
The only other thing we can really do to the equation (2) i.e., \[2x = 2x\] is to divide it both sides by 2, which would result in \[x = x\] . A solution of this equation means that \[x\] can take any value and will still satisfy the original equation.
When you arrive at a one-variable equation such as \[2x = 2x\] , where both sides of the equation are the same, then there is a clue that \[x\] can take on any value, because both sides of the equation will always simplify to the same thing respectively.

Note: A system of linear equations has infinite solutions when the equations make up the exact same line.
To solve systems of equations in two or three variables, we need to determine first whether the equation is consistent, inconsistent, independent, or dependent. A pair of linear equations, which has a unique or infinite solution are said to be a consistent pair of linear equations.