Solve The Equation:$\[ -\frac{1}{5} A + 21 = 23 \\]

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Introduction

Solving equations is a fundamental concept in mathematics, and it's essential to understand how to approach and solve them. In this article, we will focus on solving a specific equation, which is given as:

−15a+21=23{ -\frac{1}{5} a + 21 = 23 }

This equation involves a variable 'a' and a constant term. Our goal is to isolate the variable 'a' and find its value.

Understanding the Equation

Before we start solving the equation, let's break it down and understand its components. The equation is in the form of a linear equation, which means it can be written in the slope-intercept form (y = mx + b), where 'm' is the slope and 'b' is the y-intercept.

In this equation, the variable 'a' is multiplied by a fraction (-1/5), and the constant term is 21. The equation is set equal to 23, which means we need to find the value of 'a' that makes the equation true.

Isolating the Variable 'a'

To isolate the variable 'a', we need to get rid of the fraction and the constant term. We can do this by using the following steps:

  1. Subtract 21 from both sides: This will help us get rid of the constant term on the left side of the equation.

−15a+21−21=23−21{ -\frac{1}{5} a + 21 - 21 = 23 - 21 }

This simplifies to:

−15a=2{ -\frac{1}{5} a = 2 }

  1. Multiply both sides by -5: This will help us get rid of the fraction on the left side of the equation.

(−15a)×(−5)=2×(−5){ (-\frac{1}{5} a) \times (-5) = 2 \times (-5) }

This simplifies to:

a=−10{ a = -10 }

Conclusion

In this article, we solved the equation:

−15a+21=23{ -\frac{1}{5} a + 21 = 23 }

By following the steps outlined above, we were able to isolate the variable 'a' and find its value, which is -10.

Tips and Tricks

When solving equations, it's essential to follow the order of operations (PEMDAS):

  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.

By following these steps and using the correct order of operations, you can solve equations with confidence.

Real-World Applications

Solving equations is a fundamental concept in mathematics, and it has numerous real-world applications. Some examples include:

  • Physics: Solving equations is essential in physics to describe the motion of objects and predict their behavior.
  • Engineering: Solving equations is used in engineering to design and optimize systems, such as bridges and buildings.
  • Economics: Solving equations is used in economics to model economic systems and make predictions about economic trends.

In conclusion, solving equations is a critical skill in mathematics, and it has numerous real-world applications. By following the steps outlined above and using the correct order of operations, you can solve equations with confidence.

Frequently Asked Questions

Q: What is the value of 'a' in the equation?

A: The value of 'a' is -10.

Q: How do I solve equations with fractions?

A: To solve equations with fractions, you can multiply both sides of the equation by the denominator of the fraction to get rid of the fraction.

Q: What is the order of operations?

A: The order of operations is:

  1. Parentheses
  2. Exponents
  3. Multiplication and Division
  4. Addition and Subtraction

By following these steps, you can solve equations with confidence.

Additional Resources

If you're looking for additional resources to help you learn how to solve equations, here are a few suggestions:

  • Math textbooks: There are many math textbooks available that cover the basics of solving equations.
  • Online resources: Websites such as Khan Academy and Mathway offer video lessons and interactive exercises to help you learn how to solve equations.
  • Practice problems: Practice solving equations by working on problems from your textbook or online resources.

By following these steps and using the correct order of operations, you can solve equations with confidence.

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Introduction

Solving equations is a fundamental concept in mathematics, and it's essential to understand how to approach and solve them. In this article, we will focus on providing a Q&A guide to help you understand how to solve equations.

Frequently Asked Questions

Q: What is the first step in solving an equation?

A: The first step in solving an equation is to read and understand the equation. This includes identifying the variable, the constant term, and any coefficients.

Q: How do I isolate the variable in an equation?

A: To isolate the variable, you need to get rid of any coefficients or constant terms that are attached to the variable. This can be done by adding or subtracting the same value to both sides of the equation.

Q: What is the order of operations?

A: 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 solve equations with fractions?

A: To solve equations with fractions, you can multiply both sides of the equation by the denominator of the fraction to get rid of the fraction.

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 is 1, while a quadratic equation is an equation in which the highest power of the variable is 2.

Q: How do I solve quadratic equations?

A: To solve quadratic equations, you can use the quadratic formula:

x=−b±b2−4ac2a{ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} }

This formula will give you two possible solutions for the equation.

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

A: The variable in an equation represents a value that can change. The variable is often represented by a letter, such as x or y.

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

A: To check your solution to an equation, you can plug the solution back into the original equation and see if it is true.

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
  • Not isolating the variable correctly
  • Not checking the solution

Tips and Tricks

When solving equations, it's essential to follow the order of operations and to isolate the variable correctly. Here are some additional tips and tricks to help you solve equations:

  • Use a pencil: It's a good idea to use a pencil when solving equations, as you can easily erase any mistakes.
  • Read the equation carefully: Before you start solving an equation, read it carefully to make sure you understand what it's asking for.
  • Check your work: Always check your work to make sure you've solved the equation correctly.

Real-World Applications

Solving equations is a fundamental concept in mathematics, and it has numerous real-world applications. Some examples include:

  • Physics: Solving equations is essential in physics to describe the motion of objects and predict their behavior.
  • Engineering: Solving equations is used in engineering to design and optimize systems, such as bridges and buildings.
  • Economics: Solving equations is used in economics to model economic systems and make predictions about economic trends.

Conclusion

Solving equations is a critical skill in mathematics, and it has numerous real-world applications. By following the steps outlined in this article and using the correct order of operations, you can solve equations with confidence.

Additional Resources

If you're looking for additional resources to help you learn how to solve equations, here are a few suggestions:

  • Math textbooks: There are many math textbooks available that cover the basics of solving equations.
  • Online resources: Websites such as Khan Academy and Mathway offer video lessons and interactive exercises to help you learn how to solve equations.
  • Practice problems: Practice solving equations by working on problems from your textbook or online resources.

By following these steps and using the correct order of operations, you can solve equations with confidence.