What Is The Value Of $p$ In The Linear Equation $24p + 12 - 18p = 10 + 2p - 6$?A. $-4$ B. $-2$ C. $2$ D. $4$
Introduction to Linear Equations
Linear equations are a fundamental concept in mathematics, and they play a crucial role in various fields such as physics, engineering, and economics. A linear equation is an equation in which the highest power of the variable(s) is 1. In this article, we will focus on solving a linear equation to find the value of the variable $p$.
Understanding the Given Equation
The given equation is $24p + 12 - 18p = 10 + 2p - 6$. To solve for $p$, we need to isolate the variable on one side of the equation. The first step is to simplify the equation by combining like terms.
Simplifying the Equation
Let's simplify the equation by combining like terms:
Isolating the Variable
Now, let's isolate the variable $p$ by moving all the terms containing $p$ to one side of the equation and the constant terms to the other side.
Solving for $p$
To solve for $p$, we need to isolate the variable on one side of the equation. Let's subtract 12 from both sides of the equation:
Finding the Value of $p$
Now, let's find the value of $p$ by dividing both sides of the equation by 4:
Conclusion
In this article, we solved a linear equation to find the value of the variable $p$. We started by simplifying the equation, isolating the variable, and then solving for $p$. The final answer is $p = -2$.
Final Answer
The final answer is $\boxed{-2}$.
Introduction
Linear equations are a fundamental concept in mathematics, and they play a crucial role in various fields such as physics, engineering, and economics. In this article, we will answer some frequently asked questions (FAQs) on linear equations to help you better understand this concept.
Q: What is a linear equation?
A: A linear equation is an equation in which the highest power of the variable(s) is 1. It can be written in the form of $ax + b = c$, where $a$, $b$, and $c$ are constants, and $x$ is the variable.
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. You can do this by adding, subtracting, multiplying, or dividing 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(s) is 1, while a quadratic equation is an equation in which the highest power of the variable(s) is 2. For example, $2x + 3 = 5$ is a linear equation, while $x^2 + 4x + 4 = 0$ is a quadratic equation.
Q: Can I use algebraic methods to solve linear equations?
A: Yes, you can use algebraic methods such as addition, subtraction, multiplication, and division to solve linear equations. You can also use inverse operations to isolate the variable.
Q: How do I check my solution to a linear equation?
A: To check your solution to a linear equation, you need to substitute the value of the variable back into the original equation and see if it is true. If it is true, then your solution is correct.
Q: Can I use linear equations to model real-world problems?
A: Yes, you can use linear equations to model real-world problems such as cost, revenue, and profit. For example, if you have a business and you want to know how much profit you will make if you sell a certain number of products, you can use a linear equation to model the situation.
Q: What are some common applications of linear equations?
A: Some common applications of linear equations include:
- Cost and revenue problems
- Profit and loss problems
- Distance and rate problems
- Time and work problems
- Graphing and charting problems
Q: Can I use linear equations to solve systems of equations?
A: Yes, you can use linear equations to solve systems of equations. A system of equations is a set of two or more linear equations that have the same variables. You can use substitution or elimination methods to solve systems of equations.
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 using inverse operations
- Not checking your solution
- Not using algebraic methods
Conclusion
In this article, we answered some frequently asked questions (FAQs) on linear equations to help you better understand this concept. We covered topics such as what is a linear equation, how to solve a linear equation, and common applications of linear equations. We also discussed some common mistakes to avoid when solving linear equations.
Final Answer
The final answer is that linear equations are a fundamental concept in mathematics that can be used to model real-world problems and solve systems of equations.