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Chapter 1: Problem 9

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

Short Answer

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

Step by step solution

01

Applying Commutative Property of Addition

The given expression is \(5 + 3x\). According to the Commutative Property of Addition, the order of the addends can be changed without affecting the sum. So, \(5 + 3x\) can be rewritten as \(3x + 5\).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

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.

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Most popular questions from this chapter

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. The algebraic expression \(\frac{6 x+6}{x+1}\) cannot have the same value when two different replacements are made for \(x\) such as \(x=-3\) and \(x=2\)

In Exercises \(109-116\), write a numerical expression for each phrase. Then simplify the numerical expression by performing the given operations. 8 added to the product of 4 and \(-10\)

Why is it that 0 has no multiplicative inverse?

In Exercises \(109-116\), write a numerical expression for each phrase. Then simplify the numerical expression by performing the given operations. The quotient of \(-18\) and the sum of \(-15\) and 12

In Exercises \(109-116\), write a numerical expression for each phrase. Then simplify the numerical expression by performing the given operations. The quotient of \(-25\) and the sum of \(-21\) and 16
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