Problem 69 - Elementary and Intermediate Algebra

Question

Combine like terms. \(5 a+(-8 a)\)

Step-by-Step Solution

Answer

-3a

Step 1 - Identify the terms

Identify the like terms in the given expression: In this case, the terms are both involving the variable 'a': 5a and -8a.

Step 2 - Combine the coefficients

Add the coefficients of like terms together: Here, you have 5 and -8. So, calculate 5 + (-8).

Step 3 - Simplify the expression

Perform the addition: 5 + (-8) = -3. Therefore, the combined term is -3a.

Key Concepts

Algebraic Expressions

An algebraic expression is a combination of constants, variables, and operators such as addition, subtraction, multiplication, and division. For instance, in our exercise, we see the expression: 5a + (-8a).
- **Constants** are fixed values, like 5 or -8.
- **Variables** are symbols that represent numbers, in this case, 'a'.
The goal when dealing with algebraic expressions often involves simplifying or solving them to find the value of the variable. Understanding the components of an algebraic expression helps in effectively combining like terms.

Coefficients

Coefficients are the numerical part of terms that multiply the variable. In the given exercise, 5 is the coefficient of 'a' in 5a, and -8 is the coefficient of 'a' in -8a.
- Coefficients can be positive or negative.
- They dictate how many times the variable is multiplied.
When combining like terms, you are essentially summing the coefficients. In our worked example: Combining 5 (coefficient of the first term) and -8 (coefficient of the second term) gives us -3. The resulting term is -3a.

Simplifying Expressions

Simplifying an algebraic expression means reducing it to its simplest form. This involves
- Combining like terms.
- Performing arithmetic operations such as addition or subtraction.
Using our exercise, to simplify 5a + (-8a), we
1. Identify that both terms are like terms because they both involve 'a'.
2. Combine their coefficients: 5 + (-8), which equals -3.
Thus, the simplified expression is -3a.
Simplifying expressions makes them easier to understand and work with in further calculations.