Problem 34 - Beginning and Intermediate Algebra

Question

In each term, give the numerical coefficient. 15

Step-by-Step Solution

Answer

The numerical coefficient is 15.

Step 1: Identify the term

First, identify the term which needs to be evaluated. In this case, the term is simply '15'.

Step 2: Recognize the structure of the term

Notice that the term '15' is a standalone number without any variables attached to it. It can be considered as a constant term.

Step 3: Identify the numerical coefficient

The numerical coefficient of a term that is a standalone number (constant term) is the number itself. Therefore, the numerical coefficient of '15' is '15'.

Key Concepts

constant term

In algebra, a constant term is a term that has a fixed value, meaning it does not change.
It does not have any variables attached to it.
For instance, in the term '15' from our exercise, '15' is a number that stands alone.
It is constant whether you are solving an equation or simply evaluating the term.

Here are some key points to remember about constant terms:

• Constant terms do not change regardless of the values of the variables in an expression
• They can be positive, negative, or zero
• They are simply numbers

Understanding the concept of constant terms can help simplify many algebraic expressions and make problem-solving easier.

algebraic terms

Algebraic terms are parts of algebraic expressions that are separated by addition or subtraction.
A term can be a single number, a variable, or numbers and variables multiplied together.
For example, in the expression \(3x + 5y - 7\), there are three terms: '3x', '5y', and '-7'.
Each term has its own part:

• Numerical coefficient: The number part of the term, like '3' in '3x'
• Variable: The letter part, like 'x' in '3x'
• Constant term: If the term is a standalone number, it is considered a constant, like '-7'

Recognizing these parts is essential for simplifying and solving algebraic expressions.

evaluating expressions

Evaluating expressions means finding the value of an algebraic expression when the variables are known.
Here is how you can evaluate a simple expression:

• Substitute the known values of the variables into the expression
• Perform the arithmetic operations following the proper order of operations (PEMDAS/BODMAS)
• Simplify the expression to find the numerical result

For example, if you have the expression \(2x + 3\) and know that \(x = 4\), you substitute \(4\) for \(x\):
\(2(4) + 3 = 8 + 3 = 11\).
This way, evaluating expressions helps in finding specific values and understanding the relationships between different parts of the expression.