Step 1: Combine Like Terms

As we learned in the last unit, like terms are terms that contain the same variable or group of variables raised to the same exponent, regardless of their numerical coefficient. Keeping in mind that an equation is a mathematical statement that two expressions are equal,in this step we will focus on combining like terms for the two expressions contained in an equation. Since this unit deals only with equations containing a single variable, there are not many like terms to deal with. Let's look at an example. If we are given the equation 3z + 5 +2z = 12 + 3z, we need to first combine like terms in each expression of this equation.
|| The two expressions in this equation are3z + 5 +2z and12 + 4z.
3z + 5 +2z = 12 + 4z
There are three terms that contain the variable z: 3z, 2z, and 4z. We combine 3z, and 2z on the left side of the equation, then subtract 4z from both sides.
(3z +2z) + 5 = 12 + 4z5z + 5 – 4z = 12 + 4z – 4zz + 5 = 12

Notice we chose to subtract 4z from both sides rather than 5z. We chose to do this because consolidating in this manner left z positive. However, subtracting 5z from both sides would also be correct.
See how it works when we subtract 5z
from both sides 5z + 5 – 5z = 12 + 4z – 5z 5 = 12 – z