Problem 3 - Algebra 2

Question

Write a verbal expression to represent each equation. $$ 9 n-3=6 $$

Step-by-Step Solution

Answer

Nine times a number minus three equals six.

Step 1: Analyze the Equation

The equation given is $9n - 3 = 6$. It represents a mathematical statement where the product of the number 9 and the variable $n$, decreased by 3, is equal to 6.

Step 2: Identify Key Operations

In the equation, there are two operations: multiplication and subtraction. The variable $n$ is multiplied by 9, and then 3 is subtracted from the result.

Step 3: Write the Verbal Expression

The verbal expression for the equation $9n - 3 = 6$ is: "Nine times a number minus three equals six." In this expression, "a number" refers to the variable $n$ being used in the equation.

Key Concepts

Understanding Equations

Equations are like math sentences. They show a relationship between different numbers and variables using an equals sign. On one side of the equation, you have an expression, and on the other, the expression is equated to a value. This means both sides of the equation are equal to each other. For example, in the equation \(9n - 3 = 6\), the equals sign tells us that whatever we get from \(9n - 3\) will be the same as 6. So, equations help us understand how certain numbers or variables relate to one another. They often stem from real-world situations that we try to model mathematically.Equations can be simple, like \(x + 2 = 5\), where you're just adding to find the value of \(x\). Or they can be more complex, involving multiple operations like multiplication and division.

Exploring Mathematical Operations

Mathematical operations are processes you perform on numbers to manipulate them. The four basic operations are addition, subtraction, multiplication, and division. Each operation has its own symbol and rules that help us solve different problems. In the given equation \(9n - 3 = 6\), we deal with two important operations: multiplication and subtraction. Let's break it down:

• Multiplication: Here, 9 is multiplied by the variable \(n\). It means we have "nine times \(n\)." This operation is represented by writing the number next to the variable, without using a symbol, meaning \(9n\) implies 9 times \(n\).
• Subtraction: After multiplying, 3 is subtracted from the product \(9n\). Another way to think of this is removing 3 from the product. This operation is represented by the minus sign \(-\).

Understanding how these operations work together helps you convert an equation into a verbal statement or to solve for unknown variables.

Demystifying Algebraic Expressions

Algebraic expressions combine numbers, variables, and arithmetic operations into a meaningful phrase. These expressions don't have an equals sign like equations do, and they are used to represent values that can change. For instance, in the expression \(9n - 3\), "9n" is the term where 9 is the coefficient (the number you multiply a variable by) and \(n\) is the variable that can be any number. The entire expression "9n - 3" tells us to multiply \(n\) by 9 and then subtract 3 from the total product. Algebraic expressions are essential as they form the backbone of equations. They allow us to translate everyday situations into a mathematical framework which, through equations, can be analyzed to find solutions. By understanding the structure and conventions of algebraic expressions, we gain tools to speak the language of algebra fluently, making it easier to solve everyday problems.