Problem 85 - Elementary Algebra Within Reach

Question

$$ \text { Is } 3 x \text { a term of } 4-3 x \text { ? Explain. } $$

Step-by-Step Solution

Answer

No, \(3x\) is not a term of \(4-3x\). Because the sign in front of \(3x\) does matter in terms. The two terms of \(4-3x\) are \(4\) and \(-3x\), not \(3x\).

Step 1: Recognize the terms

Recognize the terms in the expression \(4 - 3x\). This expression has two terms: \(4\) and \(-3x\).

Step 2: Comparing the term

Compare the term \(3x\) with the terms in step 1. Note they are not the same, because \(3x\) is not the same as \(-3x\).

Key Concepts

Algebraic Expressions

An algebraic expression is a mathematical phrase that can include numbers, variables, and operation symbols. It's like a sentence that conveys a mathematical idea, but instead of using words, it uses mathematical symbols. For example, the expression 4 - 3x tells us that the number 4 is being subtracted by three times some variable x.

These expressions are the foundation of algebra and help us describe relationships and solve problems. Think of them as recipes that can be followed to get a result, but instead of ingredients, we have numbers and variables.

Terms in Algebra

In algebra, a term is a single mathematical entity that can be a number, a variable, or the product (or quotient) of numbers and variables. In the expression 4 - 3x, there are two terms: 4 and -3x.

Understanding that terms are like building blocks is crucial. They are the separate chunks that, when put together, make up an algebraic expression. Each term has its own identity and combining terms is like building something, piece by piece. In teaching terms in algebra, it's important to recognize that each term is distinct and follows its own rules for how it can be combined or manipulated with other terms.

Comparing Algebraic Terms

Comparing algebraic terms is a bit like comparing apples and oranges; they need to be of the same type to be comparable. In our example, 3x and -3x might look similar, but they are different because of the signs.

To compare terms:

• Look at the coefficients (the numbers in front of the variables). Here, 3x has a coefficient of 3, while -3x has a coefficient of -3.
• Consider the variables and their exponents. Both terms have an x, so they're like terms in that regard.
• However, because the coefficients differ in sign, the terms are not identical, thus not comparable as equals.

When comparing, watch for these subtle differences; they can change the entire meaning of an expression, much like a single word can change the message in a sentence.