What Value Of $q$ Is A Solution To This Equation?$-16 = 8q - 4q$ A. $ Q = − 4 Q = -4 Q = − 4 [/tex] B. $q = 4$

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Introduction

In mathematics, solving equations is a fundamental concept that helps us find the value of unknown variables. In this article, we will focus on solving a simple linear equation to determine the value of q. The equation given is -16 = 8q - 4q. We will break down the solution step by step and provide a clear explanation of the process.

Understanding the Equation

The given equation is -16 = 8q - 4q. To solve for q, we need to isolate the variable q on one side of the equation. The first step is to combine the like terms on the right-hand side of the equation.

Combining Like Terms

The equation can be rewritten as -16 = 4q. This is because the 8q and -4q are like terms, and when we combine them, we get 4q.

Isolating the Variable

Now that we have the equation -16 = 4q, we need to isolate the variable q. To do this, we can divide both sides of the equation by 4.

Solving for q

Dividing both sides of the equation by 4 gives us -16/4 = q. Simplifying the left-hand side of the equation, we get -4 = q.

Conclusion

Therefore, the value of q that is a solution to the equation -16 = 8q - 4q is q = -4.

Discussion

The solution to the equation -16 = 8q - 4q is q = -4. This means that when we substitute q = -4 into the original equation, the equation holds true. In other words, -16 = 8(-4) - 4(-4) is a true statement.

Importance of Solving Equations

Solving equations is an essential skill in mathematics and is used in various fields such as science, engineering, and economics. It helps us understand the relationships between variables and make predictions about real-world phenomena.

Real-World Applications

Solving equations has numerous real-world applications. For example, in physics, equations are used to describe the motion of objects and predict their trajectories. In economics, equations are used to model the behavior of markets and make predictions about economic trends.

Tips for Solving Equations

Here are some tips for solving equations:

  • Read the equation carefully: Before solving the equation, read it carefully to understand what is being asked.
  • Combine like terms: Combine like terms on the same side of the equation to simplify it.
  • Isolate the variable: Isolate the variable on one side of the equation by adding, subtracting, multiplying, or dividing both sides of the equation.
  • Check the solution: Check the solution by substituting it back into the original equation.

Conclusion

In conclusion, solving equations is an essential skill in mathematics that has numerous real-world applications. By following the steps outlined in this article, you can solve simple linear equations like -16 = 8q - 4q and find the value of unknown variables. Remember to read the equation carefully, combine like terms, isolate the variable, and check the solution.

Frequently Asked Questions

  • What is the value of q that is a solution to the equation -16 = 8q - 4q?
    • The value of q that is a solution to the equation -16 = 8q - 4q is q = -4.
  • How do I solve the equation -16 = 8q - 4q?
    • To solve the equation -16 = 8q - 4q, combine the like terms on the right-hand side of the equation, isolate the variable q, and check the solution.
  • What are some real-world applications of solving equations?
    • Solving equations has numerous real-world applications, including physics, economics, and engineering.

References

Introduction

Solving equations is a fundamental concept in mathematics that has numerous real-world applications. In this article, we will answer some frequently asked questions about solving equations, including tips and tricks for solving simple linear equations.

Q&A

Q: What is the value of q that is a solution to the equation -16 = 8q - 4q?

A: The value of q that is a solution to the equation -16 = 8q - 4q is q = -4.

Q: How do I solve the equation -16 = 8q - 4q?

A: To solve the equation -16 = 8q - 4q, combine the like terms on the right-hand side of the equation, isolate the variable q, and check the solution.

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

A: Solving equations has numerous real-world applications, including physics, economics, and engineering.

Q: How do I simplify a linear equation?

A: To simplify a linear equation, combine the like terms on the same side of the equation.

Q: How do I isolate the variable in a linear equation?

A: To isolate the variable in a linear equation, add, subtract, multiply, or divide both sides of the equation by the same value.

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 a quadratic equation?

A: To solve a quadratic equation, use the quadratic formula: x = (-b ± √(b^2 - 4ac)) / 2a.

Q: What is the quadratic formula?

A: The quadratic formula is a formula used to solve quadratic equations: x = (-b ± √(b^2 - 4ac)) / 2a.

Q: How do I check the solution to a linear equation?

A: To check the solution to a linear equation, substitute the solution back into the original equation and verify that 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 reading the equation carefully
  • Not combining like terms
  • Not isolating the variable
  • Not checking the solution

Tips and Tricks

  • Read the equation carefully: Before solving the equation, read it carefully to understand what is being asked.
  • Combine like terms: Combine like terms on the same side of the equation to simplify it.
  • Isolate the variable: Isolate the variable on one side of the equation by adding, subtracting, multiplying, or dividing both sides of the equation.
  • Check the solution: Check the solution by substituting it back into the original equation.

Conclusion

In conclusion, solving equations is an essential skill in mathematics that has numerous real-world applications. By following the tips and tricks outlined in this article, you can solve simple linear equations and quadratic equations with ease. Remember to read the equation carefully, combine like terms, isolate the variable, and check the solution.

Frequently Asked Questions

  • What is the value of q that is a solution to the equation -16 = 8q - 4q?
    • The value of q that is a solution to the equation -16 = 8q - 4q is q = -4.
  • How do I solve the equation -16 = 8q - 4q?
    • To solve the equation -16 = 8q - 4q, combine the like terms on the right-hand side of the equation, isolate the variable q, and check the solution.
  • What are some real-world applications of solving equations?
    • Solving equations has numerous real-world applications, including physics, economics, and engineering.

References