Algebra Equation with equals on left hand side $6 = 4 - 2x =$
Show the answer with the mechanics of working out.
 A: Equality: "$=$" is a symmetric relation, as are all equivalence relations: $$a = b \quad \overbrace{\iff}^{\text{equivalent}}\quad b = a$$ That is, it doesn't matter if we replace $\;$ "$a$ is equal to $b$" $\;$ with $\;$ "$b$ is equal to $a$:" $\;$ both expressions tell us precisely the same thing.
So, the following two equations (left hand side & right hand side of the arrow) are equivalent (meaning, really, that they give the same identical information: 
$$6 = 4 - 2x \iff 4 - 2x = 6$$

Now, I am assuming that you need to solve for $x$. Let's just go ahead and use the form of the equation you were given:


*

*$(1)$ add $+ 2x$ to each side of the equation.$$\begin{align} 6 & = 4 - 2x \\ \\ 2x + 6 & = 4 - 2x + 2x\end{align}$$ Simplify.

*$(2)$ Subtract $6$ from each side of the equation. Simplify.

*$(3)$ Divide each side of the equation by $2$. (Put differently, you can multiply each side of the equation by $\frac 12).$
A: It does not matter left or right.
We can add $2x$ on both sides to get $$6+2x=4-2x+2x$$ $$\implies 6+2x=4$$ then subtract 6 on both sides we get $$6-6+2x=4-6$$ $$\implies 2x=-2$$ then divide 2 on both sides we get $$\frac{2}{2}x=\frac{-2}{2}$$ $$\implies x=-1.$$
If we have an equation, it is "legal" to perform addition, subtraction, multiplication and division (except by 0) by equal number on both sides. Later you will also learn that it is also "legal" to take the log, power, derivative and integral and so on, on both sides.
A: Given the equation: 
$$\boxed{6=4-2x}$$
We can subtract $-4$ from both sides:
$$6-4=4-4-2x$$
Simplifying we are left with:
$$2=-2x$$
Dividing by $-2$ on both sides to isolate x:
$$\dfrac{2}{-2}=\dfrac{-2x}{-2}$$
Leaving us with the solution:
$$\boxed{x=-1}$$
We can check we have the correct solution by plugging the $-1$ back into the original equation:
$$6=4-2(-1)$$
$$6=4+2$$
$$\boxed{6=6}$$
We find the answers are the same which proves we have the correct solution.
