Problem 43 - Beginning and Intermediate Algebra

Question

Simplify each expression. \(7 y+6 y\)

Step-by-Step Solution

Answer

The simplified expression is 13y.

Step 1: Identify like terms

In the expression, identify the like terms. In this case, both terms are like terms because they both contain the variable y.

Step 2: Add the coefficients

Since the terms are like terms, add their coefficients. The coefficients of the like terms are 7 and 6.

Step 3: Simplify the expression

Add the coefficients (7 + 6) and keep the variable y. This results in 13y.

Key Concepts

Like Terms

In algebra, identifying 'like terms' is fundamental. Like terms are terms that have the same variable raised to the same power. For example, in the expression given (7y + 6y), both terms are like terms because they both contain the variable 'y' and are raised to the power of 1.
Like terms can be combined to simplify expressions, making algebraic manipulation easier.

Remember:

• Same variable
• Same exponent

Becoming adept at recognizing like terms will streamline your problem-solving process significantly.

Coefficients

When working with algebraic expressions, it's crucial to understand 'coefficients.' A coefficient is the numerical part of a term that contains a variable. In the term 7y, the number '7' is the coefficient, and in 6y, '6' is the coefficient.
The coefficients indicate how many units of the variable there are. In our example, combining these coefficients is the next step: simply add them together, 7 + 6 .

• Coefficient is the numerical part
• Indicates quantity of the variable

Adding coefficients is straightforward once you've identified the like terms.

Simplification

The final step is 'simplification,' which means making an expression as concise and efficient as possible. In our problem, after identifying like terms and their coefficients, simplifying the expression involves combining these coefficients. 7 + 6 = 13, and since the variable remains the same, you get 13y.
Simplified expressions are easier to understand and work with, especially in more complex algebraic problems.

• Combine coefficients
• Keep the variable

Simplification is all about clarity and ease, helping you to focus on solving the problem rather than getting bogged down by complex expressions.