Solve For X X X . 6 ( X − 1 ) = 9 ( X + 2 6(x-1)=9(x+2 6 ( X − 1 ) = 9 ( X + 2 ]A. X = − 8 X = -8 X = − 8 B. X = − 3 X = -3 X = − 3 C. X = 3 X = 3 X = 3 D. X = 8 X = 8 X = 8

Introduction to Linear Equations

Linear equations are a fundamental concept in mathematics, and solving them is a crucial skill for students to master. In this article, we will delve into a specific linear equation and explore the steps to solve for the variable $x$. The equation we will be working with is $6(x-1)=9(x+2)$.

Understanding the Equation

Before we begin solving the equation, let's take a closer look at its structure. The equation consists of two terms on the left-hand side and two terms on the right-hand side. The left-hand side has a coefficient of 6 multiplied by the expression $(x-1)$, while the right-hand side has a coefficient of 9 multiplied by the expression $(x+2)$. Our goal is to isolate the variable $x$ and find its value.

Distributive Property and Simplification

To solve the equation, we need to apply the distributive property, which states that for any real numbers $a$, $b$, and $c$, $a(b+c) = ab + ac$. We can use this property to expand the expressions on both sides of the equation.

6(x-1) = 6x - 6
9(x+2) = 9x + 18

Combining Like Terms

Now that we have expanded the expressions, we can combine like terms on both sides of the equation. Like terms are terms that have the same variable raised to the same power. In this case, we have the variable $x$ raised to the power of 1 on both sides of the equation.

6x - 6 = 9x + 18

Isolating the Variable

Our next step is to isolate the variable $x$ by getting all the terms with $x$ on one side of the equation and the constant terms on the other side. We can do this by subtracting $6x$ from both sides of the equation and adding 6 to both sides.

6x - 6x - 6 = 9x - 6x + 18
0 = 3x + 18

Solving for $x$

Now that we have isolated the variable $x$, we can solve for its value. To do this, we need to get rid of the constant term on the right-hand side of the equation. We can do this by subtracting 18 from both sides of the equation.

0 - 18 = 3x + 18 - 18
-18 = 3x

Final Step: Dividing by 3

Our final step is to divide both sides of the equation by 3 to solve for $x$.

-18/3 = 3x/3
-6 = x

Conclusion

In this article, we solved a linear equation of the form $6(x-1)=9(x+2)$ to find the value of the variable $x$. We applied the distributive property, combined like terms, isolated the variable, and finally solved for $x$. The value of $x$ is $-6$.

Introduction

In our previous article, we solved a linear equation of the form $6(x-1)=9(x+2)$ to find the value of the variable $x$. We applied the distributive property, combined like terms, isolated the variable, and finally solved for $x$. The value of $x$ is $-6$. In this article, we will answer some frequently asked questions related to solving linear equations.

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 $ax + b = c$, where $a$, $b$, and $c$ are constants, and $x$ is the variable.

Q: What is the distributive property?

A: The distributive property is a mathematical property that allows us to expand expressions with parentheses. It states that for any real numbers $a$, $b$, and $c$, $a(b+c) = ab + ac$.

Q: How do I combine like terms?

A: Like terms are terms that have the same variable raised to the same power. To combine like terms, we add or subtract the coefficients of the like terms. For example, $2x + 3x = (2+3)x = 5x$.

Q: How do I isolate the variable?

A: To isolate the variable, we need to get all the terms with the variable on one side of the equation and the constant terms on the other side. We can do this 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 a set of rules that tells us which operations to perform first when we have multiple operations in an expression. 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 a linear equation with fractions?

A: To solve a linear equation with fractions, we 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 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.

Q: How do I graph a linear equation?

A: To graph a linear equation, we need to find two points on the line and plot them on a coordinate plane. We can then draw a line through the two points to represent the linear equation.

Conclusion

In this article, we answered some frequently asked questions related to solving linear equations. We covered topics such as the distributive property, combining like terms, isolating the variable, and graphing linear equations. We hope that this article has been helpful in clarifying any doubts you may have had about solving linear equations.

Additional Resources

• For more information on solving linear equations, please refer to our previous article, "Solve for $x$: A Linear Equation Puzzle".
• For more information on graphing linear equations, please refer to our article, "Graphing Linear Equations: A Step-by-Step Guide".
• For more information on quadratic equations, please refer to our article, "Solving Quadratic Equations: A Step-by-Step Guide".