When you first encounter the string 3x 5 8x 3 7x 2 6x 3, it might look like a random collection of numbers and letters. Learning how to simplify algebraic expressions by combining like terms is one of the most fundamental skills in mathematics, and it serves as the gateway to solving equations, graphing functions, and understanding higher-level math. Still, in the world of algebra, this sequence represents an algebraic expression waiting to be simplified. In this guide, we will break down every part of the expression 3x + 5 + 8x + 3 + 7x + 2 + 6x + 3, explain the logic behind combining like terms, and show you how to arrive at the final simplified result step by step.
What Does 3x 5 8x 3 7x 2 6x 3 Mean?
The expression 3x 5 8x 3 7x 2 6x 3 is best understood as a series of terms added together. Although no plus signs are written between each item, the standard convention in algebra is to treat adjacent terms as part of a sum unless a subtraction sign, multiplication symbol, or other operator is specified. So, we interpret the string as:
3x + 5 + 8x + 3 + 7x + 2 + 6x + 3
This expression contains two types of terms:
- Variable terms: Terms that include the letter x, such as 3x, 8x, 7x, and 6x.
- Constant terms: Plain numbers without variables, such as 5, 3, 2, and 3.
The goal of simplifying this expression is to combine all like terms—terms that share the same variable raised to the same power—into a single, more compact expression Most people skip this — try not to. Nothing fancy..
Breaking Down the Terms: Variables, Coefficients, and Constants
Before simplifying, it helps to identify the anatomy of each term. In the term 3x:
- The letter x is the variable. It represents an unknown value that can change.
- The number 3 is the coefficient. It tells you how many copies of the variable you have.
- The entire piece 3x is a term.
In the constant 5:
- There is no variable, so 5 stands alone as a constant term. Its value does not change regardless of what x equals.
Here is the full breakdown of the expression:
| Term | Type | Variable | Coefficient |
|---|---|---|---|
| 3x | Variable term | x | 3 |
| 5 | Constant term | None | 5 |
| 8x | Variable term | x | 8 |
| 3 | Constant term | None | 3 |
| 7x | Variable term | x | 7 |
| 2 |
