Five Times The Sum Of A Number And 20 Is At Least -19 Translate The Sentence Into An Equation
Introduction
Mathematics is a fascinating subject that involves solving equations and inequalities to understand various real-world problems. In this article, we will explore the concept of translating a sentence into an equation, focusing on the given problem: "Five times the sum of a number and 20 is at least -19." We will break down the problem step by step, using mathematical concepts to arrive at the solution.
Translating the Sentence into an Equation
To translate the given sentence into an equation, we need to follow a step-by-step approach:
- Identify the key elements: The sentence contains the following key elements:
- A number (let's call it x)
- The sum of the number and 20 (x + 20)
- Five times the sum (5(x + 20))
- At least -19 (≥ -19)
- Use mathematical operations: We will use the following mathematical operations to translate the sentence:
- Addition (+)
- Multiplication (×)
- Inequality (≥)
- Write the equation: Using the key elements and mathematical operations, we can write the equation as: 5(x + 20) ≥ -19
Simplifying the Equation
To simplify the equation, we will use the distributive property of multiplication over addition:
5(x + 20) ≥ -19
Using the distributive property, we can rewrite the equation as:
5x + 100 ≥ -19
Isolating the Variable
To isolate the variable x, we need to get rid of the constant term on the left-hand side of the equation. We can do this by subtracting 100 from both sides of the equation:
5x + 100 - 100 ≥ -19 - 100
This simplifies to:
5x ≥ -119
Dividing Both Sides
To solve for x, we need to divide both sides of the equation by 5:
(5x) / 5 ≥ -119 / 5
This simplifies to:
x ≥ -23.8
Conclusion
In conclusion, the equation that represents the given sentence is:
x ≥ -23.8
This means that the sum of a number and 20, multiplied by 5, is at least -19. The solution to the equation is x ≥ -23.8, which indicates that the number x must be greater than or equal to -23.8.
Discussion
The given problem is a classic example of translating a sentence into an equation. It requires the use of mathematical operations, such as addition, multiplication, and inequality, to arrive at the solution. The problem also involves simplifying the equation, isolating the variable, and dividing both sides to solve for x.
Real-World Applications
The concept of translating a sentence into an equation has numerous real-world applications. For example, in finance, it can be used to calculate the interest on a loan or investment. In science, it can be used to model population growth or decay. In engineering, it can be used to design and optimize systems.
Tips and Tricks
Here are some tips and tricks to help you translate sentences into equations:
- Read the sentence carefully: Make sure you understand the key elements and mathematical operations involved.
- Use mathematical operations: Use addition, subtraction, multiplication, and division to translate the sentence into an equation.
- Simplify the equation: Use the distributive property and combine like terms to simplify the equation.
- Isolate the variable: Get rid of the constant term on the left-hand side of the equation by adding or subtracting the same value from both sides.
- Divide both sides: Divide both sides of the equation by the coefficient of the variable to solve for x.
Common Mistakes
Here are some common mistakes to avoid when translating sentences into equations:
- Misreading the sentence: Make sure you understand the key elements and mathematical operations involved.
- Incorrectly applying mathematical operations: Use the correct mathematical operations to translate the sentence into an equation.
- Not simplifying the equation: Simplify the equation by using the distributive property and combining like terms.
- Not isolating the variable: Get rid of the constant term on the left-hand side of the equation by adding or subtracting the same value from both sides.
- Not dividing both sides: Divide both sides of the equation by the coefficient of the variable to solve for x.
Conclusion
In conclusion, translating a sentence into an equation is a crucial skill in mathematics. It requires the use of mathematical operations, such as addition, multiplication, and inequality, to arrive at the solution. By following the steps outlined in this article, you can translate sentences into equations and solve for the variable. Remember to read the sentence carefully, use mathematical operations, simplify the equation, isolate the variable, and divide both sides to solve for x.
Introduction
In our previous article, we explored the concept of translating a sentence into an equation, focusing on the problem: "Five times the sum of a number and 20 is at least -19." We broke down the problem step by step, using mathematical concepts to arrive at the solution. In this article, we will answer some frequently asked questions related to the problem.
Q&A
Q: What is the equation that represents the given sentence?
A: The equation that represents the given sentence is:
5(x + 20) ≥ -19
Q: How do I simplify the equation?
A: To simplify the equation, you can use the distributive property of multiplication over addition:
5(x + 20) ≥ -19
Using the distributive property, you can rewrite the equation as:
5x + 100 ≥ -19
Q: How do I isolate the variable?
A: To isolate the variable x, you need to get rid of the constant term on the left-hand side of the equation. You can do this by subtracting 100 from both sides of the equation:
5x + 100 - 100 ≥ -19 - 100
This simplifies to:
5x ≥ -119
Q: How do I divide both sides of the equation?
A: To solve for x, you need to divide both sides of the equation by 5:
(5x) / 5 ≥ -119 / 5
This simplifies to:
x ≥ -23.8
Q: What is the solution to the equation?
A: The solution to the equation is x ≥ -23.8, which means that the number x must be greater than or equal to -23.8.
Q: What are some real-world applications of translating sentences into equations?
A: The concept of translating sentences into equations has numerous real-world applications, including:
- Calculating interest on a loan or investment in finance
- Modeling population growth or decay in science
- Designing and optimizing systems in engineering
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:
- Misreading the sentence
- Incorrectly applying mathematical operations
- Not simplifying the equation
- Not isolating the variable
- Not dividing both sides of the equation
Q: How can I practice translating sentences into equations?
A: You can practice translating sentences into equations by:
- Reading and understanding mathematical problems
- Using mathematical operations to translate sentences into equations
- Simplifying equations using the distributive property and combining like terms
- Isolating variables by getting rid of constant terms on the left-hand side of the equation
- Dividing both sides of the equation by the coefficient of the variable to solve for x
Conclusion
In conclusion, translating a sentence into an equation is a crucial skill in mathematics. By following the steps outlined in this article, you can translate sentences into equations and solve for the variable. Remember to read the sentence carefully, use mathematical operations, simplify the equation, isolate the variable, and divide both sides to solve for x.
Additional Resources
- For more practice problems, visit Mathway or Khan Academy.
- For a comprehensive guide to translating sentences into equations, visit Wikipedia.
Final Tips
- Practice translating sentences into equations regularly to improve your skills.
- Use online resources, such as Mathway or Khan Academy, to practice and get feedback on your work.
- Read and understand mathematical problems carefully before attempting to translate them into equations.
- Use mathematical operations, such as addition, multiplication, and inequality, to translate sentences into equations.
- Simplify equations using the distributive property and combining like terms.
- Isolate variables by getting rid of constant terms on the left-hand side of the equation.
- Divide both sides of the equation by the coefficient of the variable to solve for x.