Translate The Sentence Into An Equation.Three Less Than The Product Of 9 And A Number Is 7.Use The Variable X X X For The Unknown Number.Equation: 9 X − 3 = 7 9x - 3 = 7 9 X − 3 = 7

Introduction

Mathematics is a language that uses numbers, symbols, and equations to communicate ideas and solve problems. One of the fundamental skills in mathematics is translating sentences into equations. In this article, we will explore how to translate a sentence into an equation using a real-world example. We will use the sentence "Three less than the product of 9 and a number is 7" and translate it into an equation using the variable $x$ for the unknown number.

Understanding the Sentence

The sentence "Three less than the product of 9 and a number is 7" can be broken down into several parts:

• "Three less than" means we need to subtract 3 from the product of 9 and the number.
• "the product of 9 and a number" means we need to multiply 9 by the number.
• "is 7" means the result of the subtraction is equal to 7.

Translating the Sentence into an Equation

To translate the sentence into an equation, we need to follow the order of operations (PEMDAS):

1. Multiply 9 by the number: $9x$
2. Subtract 3 from the result: $9x - 3$
3. Set the result equal to 7: $9x - 3 = 7$

Equation: $9x - 3 = 7$

The equation $9x - 3 = 7$ represents the translation of the sentence "Three less than the product of 9 and a number is 7". This equation can be solved using algebraic methods to find the value of the unknown number $x$.

Solving the Equation

To solve the equation $9x - 3 = 7$, we need to isolate the variable $x$ on one side of the equation. We can do this by adding 3 to both sides of the equation:

$$9x - 3 + 3 = 7 + 3$$

This simplifies to:

$$9x = 10$$

Next, we can divide both sides of the equation by 9 to solve for $x$:

$$\frac{9x}{9} = \frac{10}{9}$$

This simplifies to:

$$x = \frac{10}{9}$$

Conclusion

In this article, we translated the sentence "Three less than the product of 9 and a number is 7" into an equation using the variable $x$ for the unknown number. We then solved the equation using algebraic methods to find the value of $x$. This example demonstrates the importance of translating sentences into equations in mathematics and how it can be used to solve real-world problems.

Real-World Applications

Translating sentences into equations is a fundamental skill in mathematics that has many real-world applications. Some examples include:

• Science: Scientists use equations to model and predict the behavior of physical systems, such as the motion of objects or the behavior of chemical reactions.
• Engineering: Engineers use equations to design and optimize systems, such as bridges or electronic circuits.
• Economics: Economists use equations to model and predict the behavior of economic systems, such as the behavior of supply and demand.

Tips and Tricks

Here are some tips and tricks for translating sentences into equations:

• Read the sentence carefully: Make sure you understand what the sentence is saying before you start translating it into an equation.
• Use variables: Use variables to represent unknown values in the equation.
• Follow the order of operations: Follow the order of operations (PEMDAS) when translating the sentence into an equation.
• Check your work: Check your work by plugging the solution back into the original equation to make sure it is true.

Common Mistakes

Here are some common mistakes to avoid when translating sentences into equations:

• Not reading the sentence carefully: Failing to read the sentence carefully can lead to incorrect translations.
• Not using variables: Failing to use variables can make it difficult to solve the equation.
• Not following the order of operations: Failing to follow the order of operations can lead to incorrect translations.
• Not checking your work: Failing to check your work can lead to incorrect solutions.

Conclusion

Introduction

In our previous article, we explored how to translate sentences into equations using a real-world example. In this article, we will answer some frequently asked questions about translating sentences into equations.

Q: What is the purpose of translating sentences into equations?

A: The purpose of translating sentences into equations is to represent mathematical relationships between variables in a concise and precise way. This allows us to solve problems and make predictions about real-world situations.

Q: How do I know which variable to use in an equation?

A: The variable you use in an equation should represent the unknown value in the problem. For example, if the problem asks for the number of apples in a basket, you would use the variable x to represent the number of apples.

Q: What is the order of operations (PEMDAS)?

A: The order of operations (PEMDAS) is a set of rules that tells us which operations to perform first when evaluating an expression. The acronym PEMDAS stands for:

• Parentheses: Evaluate expressions inside parentheses first.
• Exponents: Evaluate any exponential expressions next.
• Multiplication and Division: Evaluate any multiplication and division operations from left to right.
• Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

Q: How do I solve an equation with multiple variables?

A: To solve an equation with multiple variables, you need to isolate one variable on one side of the equation. You can do this by using algebraic methods such as addition, subtraction, multiplication, and division.

Q: What is the difference between an equation and an expression?

A: An equation is a statement that says two expressions are equal, while an expression is a mathematical statement that contains variables and constants. For example, the equation 2x + 3 = 5 is different from the expression 2x + 3.

Q: How do I check my work when solving an equation?

A: To check your work when solving an equation, you need to plug the solution back into the original equation to make sure it is true. This is called "back-substitution."

Q: What are some common mistakes to avoid when translating sentences into equations?

A: Some common mistakes to avoid when translating sentences into equations include:

• Not reading the sentence carefully
• Not using variables
• Not following the order of operations
• Not checking your work

Q: How can I practice translating sentences into equations?

A: You can practice translating sentences into equations by working through math problems and exercises. You can also try translating sentences from everyday life into equations to make it more interesting and challenging.

Conclusion

In conclusion, translating sentences into equations is a fundamental skill in mathematics that has many real-world applications. By following the tips and tricks outlined in this article, you can improve your skills in translating sentences into equations and solve real-world problems with confidence.

Additional Resources

If you want to learn more about translating sentences into equations, here are some additional resources you can check out:

• Math textbooks: Math textbooks often have chapters and exercises on translating sentences into equations.
• Online resources: Websites such as Khan Academy, Mathway, and Wolfram Alpha have tutorials and exercises on translating sentences into equations.
• Math apps: Math apps such as Photomath, Math Tricks, and Mathway can help you practice translating sentences into equations on the go.

Final Tips

Here are some final tips to keep in mind when translating sentences into equations:

• Practice regularly: Practice translating sentences into equations regularly to improve your skills.
• Read the sentence carefully: Read the sentence carefully to make sure you understand what it is saying.
• Use variables: Use variables to represent unknown values in the equation.
• Follow the order of operations: Follow the order of operations (PEMDAS) when translating the sentence into an equation.
• Check your work: Check your work by plugging the solution back into the original equation to make sure it is true.