Determine whether the following statement is sometimes, always, or never true: equations like 𝑎 plus 10 equals 11 and 16 minus 𝑚 equals three have only one solution.
Let’s look closely at these two equations: 𝑎 plus 10 equals 11 and 16 minus 𝑚 equals three. Here we’re dealing with addition and subtraction. The key here is that our variables are taken to the first power. We don’t have anything squared.
We don’t have any form of absolute value. And that means that there is only one solution for both 𝑎 and 𝑚. In equations like this, we often called them one-step equations. The equations will only have one solution. This statement is always true.