Always True

The opposite can happen too. Take the equation $2\left(x+1\right) = 2x+2$. Distribute the left side, and both sides become $2x+2$. Subtract $2x$ from both sides:

$$2 = 2$$

What is left is a true statement with no $x$ in it. A true statement means the original equation is true for every value of $x$. Try $x = 0$, $x = 7$ or $x = -3$, and both sides always agree. An equation like this is called an identity, and its solution is all numbers.

When the unknown cancels out, look at the statement that is left. If it is false, the equation has no solution. If it is true, every number is a solution. Both of these are complete answers.