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In algebra, terms can only be combined if they are 'like terms'. This means that the terms share the same variables raised to the same powers. Consider the terms \(-3x\) and \(+12 x\). Both of these terms contain the variable \('x'\) raised to the same power (1, which is implied), so they are recognized as like terms. Like terms allow us to simplify expressions, making them easier to work with.
Identifying like terms is crucial. Always look for all parts of your equation or expression that have the same combination of variables and powers. Oppositely, terms like \('5y'\) and \('7x'\) are not like terms because they involve different variables.
Next time you see multiple terms in an equation, ask yourself if they are 'like terms'. This first step is essential for combining them correctly.

Once you've identified like terms, the next step is combining their coefficients. A coefficient is the numerical part of a term—the number that multiplies the variable. For instance, in the term \('-3x'\), \'-3'\ is the coefficient. In \('+12x'\), the coefficient is \'12'\.
Combining coefficients means performing the mathematical operation indicated between the terms. For \(-3x + 12x\), we add the coefficients -3 and 12. Mathematically, this looks like \-3 + 12 = 9\. The result is a new coefficient: 9.
Remember, combining coefficients can involve addition, subtraction, multiplication, or division, depending on the context. However, it's most common to add or subtract them when simplifying expressions.

After combining the coefficients, don't forget about the variable itself. The variable in our example is \'x'\. Once we have the new coefficient, we reattach the variable back to this coefficient. In our case: \(-3 x + 12 x \rightarrow 9 x\). The final answer is \'9x'\.
Variables represent unknown numbers, and we often use letters like \'x'\, \'y'\, and \'z'\ to denote them. When we perform operations on like terms, the variable part remains unchanged, only the coefficients change.
Understanding how to handle variables and their coefficients will help you master algebraic expressions and equations. Practicing these steps ensures that you can simplify any problem confidently.