91Ó°ÊÓ

In algebra, **combining like terms** is a fundamental concept that helps simplify expressions. Like terms are terms that have the same variable raised to the same power. In our example expression, \(-1.8x + 2.31x\), both terms are like terms because they both contain the variable \(x\). To combine them, you just need to add their coefficients. Here's how:

1. Identify the like terms: \-1.8x and 2.31x

2. Add their coefficients: \-1.8 + 2.31 = 0.51

3. Multiply the resulting coefficient by the common variable: 0.51x

That's it! Combining like terms simplifies expressions and makes them easier to work with.

A **coefficient** is the numerical part of a term that contains both a number and a variable. In the expression \(-1.8x + 2.31x\), the coefficients are \-1.8 and 2.31. When combining like terms, you focus on adding or subtracting these coefficients.

For our example, first write down the coefficients separately:

- For the term \-1.8x, the coefficient is \-1.8
- For the term 2.31x, the coefficient is 2.31

Then, simply perform the arithmetic operation (addition, in this case) on these coefficients. So, \-1.8 + 2.31 = 0.51. Finally, multiply this result by the variable (which is x in this case), giving you the simplified expression: 0.51x.

Understanding coefficients is essential, as they dictate how much of the variable you have within the expression.

A **variable** is a symbol, usually a letter, that stands for a number we don't yet know. Variables are important in algebra because they allow us to write formulas and perform calculations that apply in many cases. In our exercise, the variable is x. Both terms in the expression \(-1.8x + 2.31x\) involve x.

Given the nature of a variable in algebra:

• It represents an unknown quantity.
• It can vary; hence the name 'variable'.
• It is essential for forming equations and expressing relationships between different quantities.

In the context of simplifying expressions, variables help us understand what the expression signifies and how changes to the variable affect the entire expression. By combining like terms and working with coefficients, we keep the variable intact so we can manipulate and solve for it effectively in different mathematical scenarios.