Translate And Solve: Ten Less Than X Is Equal To 42 . Enter The Equation First And The Solution Second

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Introduction

Linear equations are a fundamental concept in mathematics, and solving them is a crucial skill for students and professionals alike. In this article, we will focus on solving a simple linear equation, "Ten less than x is equal to 42." We will first write the equation and then provide the solution.

Writing the Equation

To write the equation, we need to translate the given statement into a mathematical expression. The statement "Ten less than x" can be translated as "x - 10." The statement "is equal to 42" can be translated as "=" followed by 42. Therefore, the equation is:

x - 10 = 42

Solution

To solve the equation, we need to isolate the variable x. We can do this by adding 10 to both sides of the equation. This will cancel out the -10 on the left side, leaving us with x alone.

x - 10 + 10 = 42 + 10

x = 52

Therefore, the solution to the equation is x = 52.

Understanding the Solution

Let's break down the solution to understand how we arrived at the answer.

  • We started with the equation x - 10 = 42.
  • We added 10 to both sides of the equation to isolate x. This is a common technique used to solve linear equations.
  • By adding 10 to both sides, we effectively canceled out the -10 on the left side, leaving us with x alone.
  • The result was x = 52, which is the solution to the equation.

Tips and Tricks

Here are some tips and tricks to help you solve linear equations like this one:

  • Always read the equation carefully and translate the words into mathematical expressions.
  • Use inverse operations to isolate the variable. In this case, we added 10 to both sides to cancel out the -10.
  • Check your work by plugging the solution back into the original equation. If the equation holds true, then you have found the correct solution.

Real-World Applications

Linear equations have many real-world applications. Here are a few examples:

  • Finance: Linear equations can be used to calculate interest rates, investment returns, and other financial metrics.
  • Science: Linear equations can be used to model population growth, chemical reactions, and other scientific phenomena.
  • Engineering: Linear equations can be used to design and optimize systems, such as bridges, buildings, and electronic circuits.

Conclusion

Solving linear equations is a fundamental skill that has many real-world applications. By following the steps outlined in this article, you can solve linear equations like "Ten less than x is equal to 42." Remember to always read the equation carefully, use inverse operations to isolate the variable, and check your work by plugging the solution back into the original equation.

Common Linear Equations

Here are some common linear equations that you may encounter:

  • x + 5 = 10: Solve for x.
  • 2x - 3 = 7: Solve for x.
  • x/2 + 2 = 5: Solve for x.

Solving Linear Equations with Fractions

Linear equations with fractions can be solved using the same techniques as linear equations with integers. Here's an example:

x/4 + 2 = 5

To solve this equation, we need to isolate x. We can do this by subtracting 2 from both sides and then multiplying both sides by 4.

x/4 = 5 - 2

x/4 = 3

x = 3 * 4

x = 12

Therefore, the solution to the equation is x = 12.

Solving Linear Equations with Decimals

Linear equations with decimals can be solved using the same techniques as linear equations with integers. Here's an example:

x + 2.5 = 7.2

To solve this equation, we need to isolate x. We can do this by subtracting 2.5 from both sides.

x = 7.2 - 2.5

x = 4.7

Therefore, the solution to the equation is x = 4.7.

Conclusion

Introduction

Linear equations are a fundamental concept in mathematics, and solving them is a crucial skill for students and professionals alike. In this article, we will provide a Q&A guide to help you understand and solve linear equations.

Q: What is a linear equation?

A: A linear equation is an equation in which the highest power of the variable (usually x) is 1. It can be written in the form ax + b = c, where a, b, and c are constants.

Q: How do I solve a linear equation?

A: To solve a linear equation, you need to isolate the variable (usually x) by using inverse operations. This can be done by adding or subtracting the same value to both sides of the equation, or by multiplying or dividing both sides by the same non-zero value.

Q: What are some common techniques for solving linear equations?

A: Some common techniques for solving linear equations include:

  • Adding or subtracting the same value to both sides of the equation
  • Multiplying or dividing both sides by the same non-zero value
  • Using inverse operations to isolate the variable
  • Checking your work by plugging the solution back into the original equation

Q: How do I handle linear equations with fractions?

A: To handle linear equations with fractions, you can use the same techniques as linear equations with integers. For example, if you have the equation x/4 + 2 = 5, you can solve it by subtracting 2 from both sides and then multiplying both sides by 4.

Q: How do I handle linear equations with decimals?

A: To handle linear equations with decimals, you can use the same techniques as linear equations with integers. For example, if you have the equation x + 2.5 = 7.2, you can solve it by subtracting 2.5 from both sides.

Q: What are some common mistakes to avoid when solving linear equations?

A: Some common mistakes to avoid when solving linear equations include:

  • Not reading the equation carefully and translating the words into mathematical expressions
  • Not using inverse operations to isolate the variable
  • Not checking your work by plugging the solution back into the original equation
  • Not being careful with signs and operations

Q: How do I check my work when solving linear equations?

A: To check your work when solving linear equations, you can plug the solution back into the original equation and see if it holds true. If the equation holds true, then you have found the correct solution.

Q: What are some real-world applications of linear equations?

A: Linear equations have many real-world applications, including:

  • Finance: Linear equations can be used to calculate interest rates, investment returns, and other financial metrics.
  • Science: Linear equations can be used to model population growth, chemical reactions, and other scientific phenomena.
  • Engineering: Linear equations can be used to design and optimize systems, such as bridges, buildings, and electronic circuits.

Q: Can you provide some examples of linear equations?

A: Here are some examples of linear equations:

  • x + 5 = 10
  • 2x - 3 = 7
  • x/2 + 2 = 5
  • x + 2.5 = 7.2

Conclusion

Solving linear equations is a fundamental skill that has many real-world applications. By following the steps outlined in this article, you can solve linear equations like "Ten less than x is equal to 42." Remember to always read the equation carefully, use inverse operations to isolate the variable, and check your work by plugging the solution back into the original equation.

Additional Resources

If you need additional help with solving linear equations, here are some additional resources:

  • Online tutorials and videos
  • Math textbooks and workbooks
  • Online math communities and forums
  • Math tutors and instructors

Conclusion

Solving linear equations is a fundamental skill that has many real-world applications. By following the steps outlined in this article, you can solve linear equations like "Ten less than x is equal to 42." Remember to always read the equation carefully, use inverse operations to isolate the variable, and check your work by plugging the solution back into the original equation.