Problem 9 - Introductory and Intermediate Algebra for College Students 4th

Question

Use the commutative property of addition to write an equivalent algebraic expression. $$5+3 x$$

Step-by-Step Solution

Answer

The equivalent algebraic expression is \(3x + 5\).

Step 1: Identify the Expression

Use the commutative property of addition to write an equivalent algebraic
expression.
$$5+3 x$$

Step 2: Apply the Required Transformation

Rewrite the expression in the requested form using the appropriate rules.

Step 3: Result

The equivalent algebraic expression is \(3x + 5\).

Key Concepts

Addition

Addition is one of the basic arithmetic operations we use every day. When adding numbers or terms together, we are combining their values to form a new total. In mathematics, especially in algebra, we often see addition used to combine numbers with variables.
For example, when you see an expression like \(5 + 3x\), it is indicating that you are adding 5 to the product of 3 and \(x\). The numbers and variables become parts of one coherent expression, and their order can be adjusted. This is especially important when dealing with operations and simplifying algebraic expressions.

Algebraic Expression

An algebraic expression is a combination of numbers, variables, and arithmetic operations like addition, subtraction, multiplication, and division. It's essential in displaying relationships and solving problems in algebra.
In the expression \(5 + 3x\), \(5\) is a constant, and \(3x\) is a term that includes the variable \(x\). Variables are symbols like \(x\) that represent unknown values. They give algebraic expressions their power, enabling us to solve for many possible values. Understanding how to manipulate these expressions by applying properties like the commutative property is crucial for simplifying and solving them efficiently.

Equivalent Expression

Equivalent expressions are different expressions that equal the same value. Finding equivalent expressions is a common task in algebra, as it helps simplify complex problems and equations.
For instance, the expression \(5 + 3x\) can be transformed into an equivalent expression \(3x + 5\). Even though they look different, these two expressions are equal. The commutative property of addition allows us to switch the order of the terms without altering the sum's value. Recognizing and creating equivalent expressions is a key skill that helps in solving algebraic equations accurately and efficiently.