What Is The Value Of $p$ In The Linear Equation $24p + 12 - 18p = 10 + 2p - 6$?A. $-4$ B. $-2$ C. $2$ D. $4$

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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 specific linear equation to find the value of $p$. We will break down the problem step by step, using algebraic techniques to isolate the variable $p$. By the end of this article, you will have a clear understanding of how to solve linear equations and find the value of unknown variables.

The Linear Equation

The given linear equation is:

24p+12−18p=10+2p−624p + 12 - 18p = 10 + 2p - 6

Our goal is to find the value of $p$ that satisfies this equation. To do this, we will use algebraic techniques to simplify the equation and isolate the variable $p$.

Step 1: Simplify the Equation

The first step in solving the equation is to simplify it by combining like terms. We can start by combining the constants on the left-hand side of the equation:

24p+12−18p=10+2p−624p + 12 - 18p = 10 + 2p - 6

6p+12=4+2p6p + 12 = 4 + 2p

Step 2: Isolate the Variable $p$

Next, we need to isolate the variable $p$ by getting all the terms containing $p$ on one side of the equation. We can do this by subtracting $2p$ from both sides of the equation:

6p+12=4+2p6p + 12 = 4 + 2p

6p−2p=4−126p - 2p = 4 - 12

4p=−84p = -8

Step 3: Solve for $p$

Now that we have isolated the variable $p$, we can solve for its value by dividing both sides of the equation by the coefficient of $p$, which is 4:

4p=−84p = -8

p=−84p = \frac{-8}{4}

p=−2p = -2

Conclusion

In this article, we solved a linear equation to find the value of $p$. We started by simplifying the equation and isolating the variable $p$, and then solved for its value by dividing both sides of the equation by the coefficient of $p$. The final answer is $p = -2$.

Why is Solving Linear Equations Important?

Solving linear equations is an essential skill in mathematics, and it has numerous applications in real-life situations. For example, linear equations are used in physics to describe the motion of objects, in economics to model the behavior of markets, and in computer science to solve problems in algorithms and data structures. By mastering the skill of solving linear equations, you will be able to tackle a wide range of problems and make informed decisions in various fields.

Tips and Tricks for Solving Linear Equations

Here are some tips and tricks to help you solve linear equations like a pro:

  • Use algebraic techniques: Linear equations can be solved using algebraic techniques such as addition, subtraction, multiplication, and division.
  • Simplify the equation: Simplify the equation by combining like terms and isolating the variable.
  • Use inverse operations: Use inverse operations such as addition and subtraction to isolate the variable.
  • Check your answer: Check your answer by plugging it back into the original equation to ensure that it is true.

Common Mistakes to Avoid

Here are some common mistakes to avoid when solving linear equations:

  • Not simplifying the equation: Failing to simplify the equation can lead to incorrect solutions.
  • Not isolating the variable: Failing to isolate the variable can lead to incorrect solutions.
  • Not checking the answer: Failing to check the answer can lead to incorrect solutions.

Conclusion

Solving linear equations is a crucial skill in mathematics, and it has numerous applications in real-life situations. By mastering the skill of solving linear equations, you will be able to tackle a wide range of problems and make informed decisions in various fields. Remember to use algebraic techniques, simplify the equation, use inverse operations, and check your answer to ensure that you get the correct solution.

Introduction

Solving linear equations is a fundamental concept in mathematics, and it can be a bit challenging for some students. In this article, we will answer some frequently asked questions (FAQs) about solving linear equations. Whether you are a student, teacher, or just someone who wants to learn more about linear equations, this article is for you.

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 is a simple equation that can be solved using algebraic techniques.

Q: How do I simplify a linear equation?

A: To simplify a linear equation, you need to combine like terms and isolate the variable. Like terms are terms that have the same variable and exponent. For example, 2x and 3x are like terms.

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. For example, 2x + 3 is a linear equation, while x^2 + 2x + 1 is a quadratic equation.

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: What is the inverse operation of addition?

A: The inverse operation of addition is subtraction. For example, if you have 2x + 3, the inverse operation is 2x - 3.

Q: How do I check my answer when solving a linear equation?

A: To check your answer, you need to plug it back into the original equation and see if it is true. If it is true, then your answer 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 simplifying the equation
  • Not isolating the variable
  • Not checking the answer
  • Using the wrong inverse operation

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

A: To solve a linear equation with decimals, you need to eliminate the decimals by multiplying both sides of the equation by 10 or 100, depending on the number of decimal places.

Q: What is the difference between a linear equation and a system of linear equations?

A: A linear equation is a single equation, while a system of linear equations is a set of two or more equations that need to be solved simultaneously.

Conclusion

Solving linear equations is a fundamental concept in mathematics, and it can be a bit challenging for some students. However, with practice and patience, you can master the skill of solving linear equations. Remember to simplify the equation, isolate the variable, and check your answer to ensure that you get the correct solution. If you have any more questions or need further clarification, feel free to ask.

Additional Resources

If you want to learn more about solving linear equations, here are some additional resources that you can use:

  • Online tutorials: There are many online tutorials and videos that can help you learn how to solve linear equations.
  • Math textbooks: Math textbooks are a great resource for learning how to solve linear equations.
  • Practice problems: Practice problems are a great way to practice solving linear equations and improve your skills.
  • Online communities: Online communities, such as math forums and social media groups, can be a great resource for getting help and feedback on solving linear equations.

Final Tips

Here are some final tips for solving linear equations:

  • Practice regularly: Practice solving linear equations regularly to improve your skills.
  • Use algebraic techniques: Use algebraic techniques, such as addition, subtraction, multiplication, and division, to solve linear equations.
  • Simplify the equation: Simplify the equation by combining like terms and isolating the variable.
  • Check your answer: Check your answer by plugging it back into the original equation to ensure that it is true.