What Is The Solution To This Equation? 3 ( 4 X + 6 ) = 9 X + 12 3(4x + 6) = 9x + 12 3 ( 4 X + 6 ) = 9 X + 12 A. X = − 2 X = -2 X = − 2 B. X = − 10 X = -10 X = − 10 C. X = 10 X = 10 X = 10 D. X = 2 X = 2 X = 2

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, $3(4x + 6) = 9x + 12$, and explore the different methods and techniques used to find the solution.

Understanding the Equation

The given equation is a linear equation in one variable, $x$. It involves a combination of constants, coefficients, and variables. To solve this equation, we need to isolate the variable $x$ and find its value.

Step 1: Distribute the Coefficient

The first step in solving the equation is to distribute the coefficient $3$ to the terms inside the parentheses.

$3(4x + 6) = 3 \times 4x + 3 \times 6$

Using the distributive property, we get:

$12x + 18 = 9x + 12$

Step 2: Simplify the Equation

Now that we have distributed the coefficient, we can simplify the equation by combining like terms.

$12x + 18 = 9x + 12$

Subtracting $9x$ from both sides gives us:

$3x + 18 = 12$

Step 3: Isolate the Variable

To isolate the variable $x$, we need to get rid of the constant term on the left-hand side. We can do this by subtracting $18$ from both sides.

$3x + 18 - 18 = 12 - 18$

This simplifies to:

$3x = -6$

Step 4: Solve for $x$

Finally, we can solve for $x$ by dividing both sides of the equation by $3$.

$\frac{3x}{3} = \frac{-6}{3}$

This gives us:

$x = -2$

Conclusion

In this article, we solved the linear equation $3(4x + 6) = 9x + 12$ using the distributive property, simplification, and isolation of the variable. We found that the solution to the equation is $x = -2$. This is a fundamental concept in mathematics, and understanding how to solve linear equations is essential for success in various fields, including science, engineering, and economics.

Answer Key

The correct answer is:

A. $x = -2$

Why is this important?

Solving linear equations is a crucial skill for students and professionals alike. It is used in various fields, including science, engineering, and economics. Understanding how to solve linear equations can help you:

• Analyze and interpret data
• Make informed decisions
• Solve real-world problems
• Develop critical thinking and problem-solving skills

Real-World Applications

Linear equations have numerous real-world applications, including:

• Physics: Solving linear equations is used to describe the motion of objects, including velocity, acceleration, and force.
• Engineering: Linear equations are used to design and optimize systems, including electrical circuits, mechanical systems, and structural analysis.
• Economics: Linear equations are used to model economic systems, including supply and demand, cost-benefit analysis, and optimization problems.

Tips and Tricks

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

• Use the distributive property to simplify the equation.
• Combine like terms to simplify the equation.
• Isolate the variable by getting rid of the constant term.
• Use inverse operations to solve for the variable.

Introduction

In our previous article, we explored the solution to the linear equation $3(4x + 6) = 9x + 12$. We used the distributive property, simplification, and isolation of the variable to find the solution, $x = -2$. In this article, we will answer some frequently asked questions about solving linear equations.

Q: What is a linear equation?

A linear equation is an equation in which the highest power of the variable is 1. It can be written in the form $ax + b = c$, where $a$, $b$, and $c$ are constants, and $x$ is the variable.

Q: How do I solve a linear equation?

To solve a linear equation, you need to isolate the variable by getting rid of the constant term. You can do this by using inverse operations, such as addition, subtraction, multiplication, and division.

Q: What is the distributive property?

The distributive property is a mathematical property that allows you to distribute a coefficient to the terms inside the parentheses. It is written as $a(b + c) = ab + ac$.

Q: How do I use the distributive property to solve a linear equation?

To use the distributive property to solve a linear equation, you need to distribute the coefficient to the terms inside the parentheses. For example, if you have the equation $3(4x + 6) = 9x + 12$, you can use the distributive property to get $12x + 18 = 9x + 12$.

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

A linear equation is an equation in which the highest power of the variable is 1. A quadratic equation is an equation in which the highest power of the variable is 2. For example, $x^2 + 4x + 4 = 0$ is a quadratic equation, while $2x + 3 = 5$ is a linear equation.

Q: How do I solve a quadratic equation?

To solve a quadratic equation, you need to use the quadratic formula, which is $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$. You can also use factoring or the quadratic formula to solve a quadratic equation.

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

Some common mistakes to avoid when solving linear equations include:

• Not using the distributive property to simplify the equation
• Not combining like terms to simplify the equation
• Not isolating the variable by getting rid of the constant term
• Not using inverse operations to solve for the variable

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

To check your solution to a linear equation, you need to plug the solution back into the original equation and see if it is true. For example, if you have the equation $2x + 3 = 5$ and you think the solution is $x = 1$, you can plug $x = 1$ back into the equation to see if it is true.

Conclusion

Solving linear equations is a crucial skill for students and professionals alike. By understanding how to solve linear equations, you can analyze and interpret data, make informed decisions, and solve real-world problems. In this article, we answered some frequently asked questions about solving linear equations and provided tips and tricks to help you become proficient in solving linear equations.

Answer Key

Here are the answers to the questions:

• Q: What is a linear equation? A: A linear equation is an equation in which the highest power of the variable is 1.
• Q: How do I solve a linear equation? A: To solve a linear equation, you need to isolate the variable by getting rid of the constant term.
• Q: What is the distributive property? A: The distributive property is a mathematical property that allows you to distribute a coefficient to the terms inside the parentheses.
• Q: How do I use the distributive property to solve a linear equation? A: To use the distributive property to solve a linear equation, you need to distribute the coefficient to the terms inside the parentheses.
• 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, you need to use the quadratic formula or factoring.
• Q: What are some common mistakes to avoid when solving linear equations? A: Some common mistakes to avoid when solving linear equations include not using the distributive property, not combining like terms, not isolating the variable, and not using inverse operations.
• Q: How do I check my solution to a linear equation? A: To check your solution to a linear equation, you need to plug the solution back into the original equation and see if it is true.