What Is The Solution To The Following Equation?$x + (-21) = 8$A. $x = 29$B. $x = 13$C. $x = 27$D. $x = 17$

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Introduction

In mathematics, solving equations is a fundamental concept that helps us find the value of unknown variables. When we encounter an equation like x+(−21)=8x + (-21) = 8, our goal is to isolate the variable xx and determine its value. In this article, we will walk through the steps to solve this equation and find the correct solution.

Understanding the Equation

The given equation is x+(−21)=8x + (-21) = 8. To solve for xx, we need to isolate the variable on one side of the equation. The equation consists of two terms: xx and −21-21. The −21-21 is a constant term that needs to be eliminated to find the value of xx.

Step 1: Add 21 to Both Sides of the Equation

To eliminate the −21-21 term, we can add 21 to both sides of the equation. This will help us get rid of the negative term and isolate the variable xx. The equation becomes:

x+(−21)+21=8+21x + (-21) + 21 = 8 + 21

Simplifying the Equation

When we add 21 to both sides of the equation, the −21-21 and +21+21 terms cancel each other out, leaving us with:

x=8+21x = 8 + 21

Evaluating the Expression

Now, we need to evaluate the expression on the right-hand side of the equation. We add 8 and 21 to get:

x=29x = 29

Conclusion

Therefore, the solution to the equation x+(−21)=8x + (-21) = 8 is x=29x = 29. This means that the value of the variable xx is 29.

Why is this the Correct Solution?

To verify that x=29x = 29 is the correct solution, we can substitute this value back into the original equation. If the equation holds true, then we have found the correct solution.

x+(−21)=8x + (-21) = 8

Substituting x=29x = 29 into the equation:

29+(−21)=829 + (-21) = 8

Evaluating the expression:

8=88 = 8

Since the equation holds true, we can conclude that x=29x = 29 is indeed the correct solution.

What if the Solution is not Among the Options?

If the solution is not among the options A, B, C, or D, it means that the solution is not correct. In this case, we need to re-evaluate our steps and ensure that we have followed the correct procedure to solve the equation.

Common Mistakes to Avoid

When solving equations, it's essential to avoid common mistakes that can lead to incorrect solutions. Some common mistakes include:

  • Not following the order of operations (PEMDAS)
  • Not isolating the variable on one side of the equation
  • Not evaluating expressions correctly
  • Not checking the solution by substituting it back into the original equation

Tips for Solving Equations

To solve equations effectively, follow these tips:

  • Read the equation carefully and understand what it's asking for
  • Identify the variable and the constant terms
  • Use inverse operations to isolate the variable
  • Check the solution by substituting it back into the original equation
  • Avoid common mistakes and double-check your work

Conclusion

Solving equations is a crucial skill in mathematics that helps us find the value of unknown variables. By following the steps outlined in this article, you can solve equations like x+(−21)=8x + (-21) = 8 and find the correct solution. Remember to avoid common mistakes, check your work, and verify the solution by substituting it back into the original equation. With practice and patience, you'll become proficient in solving equations and tackle more complex problems with confidence.

Introduction

Solving equations is a fundamental concept in mathematics that can be challenging for some students. In this article, we will address some frequently asked questions (FAQs) about solving equations, providing clarity and guidance on how to tackle these problems.

Q: What is an equation, and how do I solve it?

A: An equation is a mathematical statement that expresses the equality of two expressions. To solve an equation, you need to isolate the variable (the unknown value) on one side of the equation. This can be done by using inverse operations, such as addition and subtraction, multiplication and division.

Q: What is the order of operations (PEMDAS), and why is it important?

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

  1. Parentheses: Evaluate expressions inside parentheses first.
  2. Exponents: Evaluate any exponential expressions next.
  3. Multiplication and Division: Evaluate 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 isolate the variable on one side of the equation?

A: To isolate the variable, you need to use inverse operations to get rid of any constants or other terms that are attached to the variable. For example, if you have the equation:

x + 3 = 7

You can subtract 3 from both sides of the equation to isolate the variable:

x = 7 - 3 x = 4

Q: What is the difference between a linear equation and a quadratic equation?

A: A linear equation is an equation in which the highest power of the variable (x) is 1. For example:

2x + 3 = 5

A quadratic equation, on the other hand, is an equation in which the highest power of the variable (x) is 2. For example:

x^2 + 4x + 4 = 0

Q: How do I solve a quadratic equation?

A: To solve a quadratic equation, you can use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / 2a

where a, b, and c are the coefficients of the quadratic equation.

Q: What is the significance of the variable in an equation?

A: The variable in an equation represents the unknown value that we are trying to find. In other words, the variable is the solution to the equation.

Q: How do I check my solution to an equation?

A: To check your solution, you can substitute the value back into the original equation and see if it holds true. If the equation is true, then you have found the correct solution.

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

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

  • Not following the order of operations (PEMDAS)
  • Not isolating the variable on one side of the equation
  • Not evaluating expressions correctly
  • Not checking the solution by substituting it back into the original equation

Q: How can I practice solving equations?

A: You can practice solving equations by working through example problems, using online resources, or seeking help from a teacher or tutor.

Conclusion

Solving equations is a fundamental concept in mathematics that requires practice and patience. By following the steps outlined in this article and practicing regularly, you can become proficient in solving equations and tackle more complex problems with confidence. Remember to avoid common mistakes, check your work, and verify the solution by substituting it back into the original equation.