Example

Solve for $w: \quad \displaystyle 2(w+2)+w=3(w-1)+6$

Solution

First remove parentheses by distributing:

Now combine like terms to get

At this point, you might recognize that our original equation reduced to a contradiction. If you do not notice that, it's okay. We can continue by getting all variables on one side. In order to do so, let's subtract $3w$ from both sides. This gives the new equation

The variable $w$ has disappeared from the equation, and we are left with the never-true, nonsensical statement that $4$ is equal to $3$. The contradiction, $4=3$, indicates that the original equation was also a contradiction. The original equation has no solution.