Which Mathematical Equation Is Equivalent To The Verbal Expression Five Less Than The Quotient Of A Number And Two Is Not Equal To 7?A. $\frac{x}{2} - 5 \neq 7$B. $2x - 5 \neq 7$C. $5 - 2x \neq 7$D. $5 - \frac{x}{2}

Introduction

Mathematical equations and verbal expressions are two fundamental concepts in mathematics that often seem unrelated. However, they are deeply connected, and understanding the relationship between them is crucial for solving mathematical problems. In this article, we will delve into the world of mathematical equations and verbal expressions, focusing on the verbal expression "Five less than the quotient of a number and two is not equal to 7." Our goal is to identify the equivalent mathematical equation among the given options.

Understanding Verbal Expressions

A verbal expression is a mathematical statement that uses words to describe a mathematical relationship. It is a way of expressing a mathematical concept using natural language. Verbal expressions can be complex and may involve various mathematical operations, such as addition, subtraction, multiplication, and division.

Breaking Down the Verbal Expression

The verbal expression "Five less than the quotient of a number and two is not equal to 7" can be broken down into smaller parts to understand its meaning. Let's analyze each part:

• "Five less than": This phrase indicates that we need to subtract 5 from the result of the next operation.
• "the quotient of a number and two": This phrase indicates that we need to divide a number by 2.
• "is not equal to 7": This phrase indicates that the result of the previous operation should not be equal to 7.

Translating the Verbal Expression into a Mathematical Equation

Now that we have broken down the verbal expression, let's translate it into a mathematical equation. We will use the following steps:

1. Identify the unknown variable: In this case, the unknown variable is the number that we are trying to find.
2. Translate the verbal expression into a mathematical expression: We will use the words in the verbal expression to create a mathematical expression.
3. Simplify the mathematical expression: We will simplify the mathematical expression to make it easier to work with.

Step 1: Identify the Unknown Variable

The unknown variable is the number that we are trying to find. Let's call it x.

Step 2: Translate the Verbal Expression into a Mathematical Expression

The verbal expression "Five less than the quotient of a number and two is not equal to 7" can be translated into a mathematical expression as follows:

• "the quotient of a number and two" can be translated into a mathematical expression as x/2.
• "five less than" can be translated into a mathematical expression as -5.
• "is not equal to 7" can be translated into a mathematical expression as ≠ 7.

Therefore, the mathematical expression is x/2 - 5 ≠ 7.

Step 3: Simplify the Mathematical Expression

The mathematical expression x/2 - 5 ≠ 7 can be simplified by multiplying both sides of the inequality by 2 to eliminate the fraction. This gives us:

x - 10 ≠ 14

Comparing the Mathematical Expression with the Given Options

Now that we have simplified the mathematical expression, let's compare it with the given options:

A. $\frac{x}{2} - 5 \neq 7$ B. $2x - 5 \neq 7$ C. $5 - 2x \neq 7$ D. $5 - \frac{x}{2} \neq 7$

The only option that matches our simplified mathematical expression is option A: $\frac{x}{2} - 5 \neq 7$.

Conclusion

In this article, we have explored the relationship between mathematical equations and verbal expressions. We have taken a verbal expression "Five less than the quotient of a number and two is not equal to 7" and translated it into a mathematical equation. We have also compared the mathematical equation with the given options and identified the correct answer.

Final Answer

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Q&A: Frequently Asked Questions about Mathematical Equations and Verbal Expressions

Introduction

In our previous article, we explored the relationship between mathematical equations and verbal expressions. We took a verbal expression "Five less than the quotient of a number and two is not equal to 7" and translated it into a mathematical equation. In this article, we will answer some frequently asked questions about mathematical equations and verbal expressions.

Q: What is the difference between a mathematical equation and a verbal expression?

A: A mathematical equation is a statement that expresses the equality of two mathematical expressions, while a verbal expression is a mathematical statement that uses words to describe a mathematical relationship.

Q: How do I translate a verbal expression into a mathematical equation?

A: To translate a verbal expression into a mathematical equation, follow these steps:

1. Identify the unknown variable.
2. Translate the verbal expression into a mathematical expression.
3. Simplify the mathematical expression.

Q: What are some common verbal expressions that can be translated into mathematical equations?

A: Some common verbal expressions that can be translated into mathematical equations include:

• "Five less than the quotient of a number and two is not equal to 7"
• "The sum of a number and three is greater than 10"
• "The difference between a number and four is not equal to 2"

Q: How do I simplify a mathematical expression?

A: To simplify a mathematical expression, follow these steps:

1. Combine like terms.
2. Eliminate any fractions by multiplying both sides of the equation by the denominator.
3. Use the distributive property to expand any parentheses.

Q: What are some common mistakes to avoid when translating verbal expressions into mathematical equations?

A: Some common mistakes to avoid when translating verbal expressions into mathematical equations include:

• Misinterpreting the order of operations.
• Failing to identify the unknown variable.
• Not simplifying the mathematical expression.

Q: How do I determine if a mathematical equation is equivalent to a verbal expression?

A: To determine if a mathematical equation is equivalent to a verbal expression, follow these steps:

1. Translate the verbal expression into a mathematical equation.
2. Compare the mathematical equation with the given options.
3. Check if the mathematical equation matches the verbal expression.

Q: What are some real-world applications of mathematical equations and verbal expressions?

A: Some real-world applications of mathematical equations and verbal expressions include:

• Solving problems in physics and engineering.
• Modeling population growth and decline.
• Analyzing data in finance and economics.

Conclusion

In this article, we have answered some frequently asked questions about mathematical equations and verbal expressions. We have provided tips and tricks for translating verbal expressions into mathematical equations and simplifying mathematical expressions. We have also discussed some common mistakes to avoid and real-world applications of mathematical equations and verbal expressions.

Final Answer

The final answer is that mathematical equations and verbal expressions are two fundamental concepts in mathematics that are deeply connected. Understanding the relationship between them is crucial for solving mathematical problems and applying mathematical concepts to real-world situations.