Solve For \[$ X \$\] In The Equation:$\[ X + 16 = 24 \\]Is \[$ X = 8 \$\] The Correct Solution? Choose The Correct Answer Below:A. No, Because Both Sides Evaluate To Nonzero.B. Yes, Because Both Sides Evaluate To Zero.C. Yes,

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Introduction

Linear equations are a fundamental concept in mathematics, and solving them is a crucial skill for students to master. In this article, we will focus on solving a simple linear equation and determine if a given solution is correct. We will use the equation x+16=24x + 16 = 24 as an example and explore the steps involved in solving it.

Understanding the Equation

The given equation is x+16=24x + 16 = 24. This is a linear equation in one variable, where xx is the variable we need to solve for. The equation states that the sum of xx and 1616 is equal to 2424.

Step 1: Isolate the Variable

To solve for xx, we need to isolate the variable on one side of the equation. In this case, we can subtract 1616 from both sides of the equation to get:

x+16−16=24−16x + 16 - 16 = 24 - 16

This simplifies to:

x=8x = 8

Step 2: Check the Solution

Now that we have solved for xx, we need to check if the solution is correct. To do this, we can substitute the value of xx back into the original equation and see if it is true.

x+16=24x + 16 = 24

Substituting x=8x = 8 into the equation, we get:

8+16=248 + 16 = 24

This is indeed true, so we can conclude that x=8x = 8 is the correct solution.

Conclusion

In this article, we solved a simple linear equation and determined if a given solution was correct. We used the equation x+16=24x + 16 = 24 as an example and explored the steps involved in solving it. By following these steps, we were able to isolate the variable and check the solution, confirming that x=8x = 8 is indeed the correct solution.

Why is this Solution Correct?

The solution x=8x = 8 is correct because it satisfies the original equation. When we substitute x=8x = 8 into the equation, we get:

8+16=248 + 16 = 24

This is true, so we can conclude that x=8x = 8 is the correct solution.

What if the Solution was Incorrect?

If the solution was incorrect, we would need to re-examine the steps involved in solving the equation. We would need to check if we made any mistakes when isolating the variable or checking the solution.

Common Mistakes to Avoid

When solving linear equations, there are several common mistakes to avoid. These include:

  • Not isolating the variable: Make sure to isolate the variable on one side of the equation.
  • Not checking the solution: Always check the solution by substituting the value of the variable back into the original equation.
  • Making arithmetic errors: Double-check your arithmetic to ensure that you are not making any mistakes.

Real-World Applications

Linear equations have many real-world applications. Some examples include:

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

Conclusion

In conclusion, solving linear equations is a crucial skill for students to master. By following the steps involved in solving an equation, we can isolate the variable and check the solution, confirming that the solution is correct. Linear equations have many real-world applications, and understanding how to solve them is essential for success in mathematics and other fields.

Final Thoughts

Solving linear equations is a fundamental concept in mathematics, and it is essential to understand how to solve them. By following the steps involved in solving an equation, we can isolate the variable and check the solution, confirming that the solution is correct. With practice and patience, anyone can master the art of solving linear equations.

References

Additional Resources

Introduction

Linear equations are a fundamental concept in mathematics, and solving them is a crucial skill for students to master. In this article, we will provide a Q&A guide to help students understand how to solve linear equations and address common questions and concerns.

Q: What is a linear equation?

A: A linear equation is an equation in which the highest power of the variable is 1. It is a simple equation that can be solved using basic algebraic operations.

Q: How do I solve a linear equation?

A: To solve a linear equation, you need to isolate the variable on one side of the equation. This can be done by adding, subtracting, multiplying, or dividing both sides of the equation by the same value.

Q: What is the order of operations?

A: The order of operations is a set of rules that dictate the order in which mathematical operations should be performed. The order of operations is:

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

Q: How do I check my solution?

A: To check your solution, substitute the value of the variable back into the original equation and see if it is true. If the equation is true, then your solution is correct.

Q: What if I get a negative solution?

A: If you get a negative solution, it means that the variable is not a positive number. However, in some cases, a negative solution can be a valid solution. For example, if the equation is x−5=3x - 5 = 3, then the solution is x=8x = 8, which is a positive number. However, if the equation is x+5=3x + 5 = 3, then the solution is x=−2x = -2, which is a negative number.

Q: Can I use a calculator to solve linear equations?

A: Yes, you can use a calculator to solve linear equations. However, it is always a good idea to check your solution by hand to ensure that it is correct.

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

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

  • Not isolating the variable
  • Not checking the solution
  • Making arithmetic errors
  • Not following the order of operations

Q: How do I solve a linear equation with fractions?

A: To solve a linear equation with fractions, you need to eliminate the fractions by multiplying both sides of the equation by the least common multiple (LCM) of the denominators.

Q: Can I solve a linear equation with decimals?

A: Yes, you can solve a linear equation with decimals. However, it is always a good idea to round the decimal values to the nearest whole number to make the calculation easier.

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

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

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

Conclusion

In conclusion, solving linear equations is a crucial skill for students to master. By following the steps involved in solving an equation, we can isolate the variable and check the solution, confirming that the solution is correct. With practice and patience, anyone can master the art of solving linear equations.

Final Thoughts

Solving linear equations is a fundamental concept in mathematics, and it is essential to understand how to solve them. By following the steps involved in solving an equation, we can isolate the variable and check the solution, confirming that the solution is correct. With practice and patience, anyone can master the art of solving linear equations.

References

Additional Resources