Example

Solve for $w: \quad \displaystyle -6(w+1)+8w=2(w-3)$

Solution

First remove parentheses by distributing:

Now combine like terms to get

At this point, you might recognize that our original equation reduced to an identity. 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 $2w$ from both sides. This gives the new equation

The variable $w$ has disappeared from the equation, and we are left with the always-true, identity $-6=-6$. This identity indicates that the original equation was also an identity. Every number is a solution, and the equation has infinitely many solutions.