What Is The Solution To This Equation?$8x - 5(x - 3) = 18$A. $x = 1$ B. $x = 11$ C. $x = 7$ D. $x = 5$

$$

Introduction

In mathematics, solving equations is a fundamental concept that helps us find the value of unknown variables. Equations are statements that express the equality of two mathematical expressions. In this article, we will focus on solving a linear equation of the form $8x - 5(x - 3) = 18$. We will use algebraic techniques to simplify the equation and find the value of the variable $x$.

Understanding the Equation

The given equation is $8x - 5(x - 3) = 18$. To solve this equation, we need to simplify it by applying the distributive property and combining like terms. The distributive property states that for any real numbers $a$, $b$, and $c$, $a(b + c) = ab + ac$. We can use this property to expand the expression $-5(x - 3)$.

Expanding the Expression

Using the distributive property, we can expand the expression $-5(x - 3)$ as follows:

$$-5(x - 3) = -5x + 15$$

Now, we can rewrite the original equation as:

$$8x - 5x + 15 = 18$$

Combining Like Terms

We can combine the like terms $8x$ and $-5x$ to simplify the equation further:

$$3x + 15 = 18$$

Isolating the Variable

To isolate the variable $x$, we need to get rid of the constant term $15$ on the left-hand side of the equation. We can do this by subtracting $15$ from both sides of the equation:

$$3x = 18 - 15$$

$$3x = 3$$

Solving for $x$

Now, we can solve for $x$ by dividing both sides of the equation by $3$:

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

$$x = 1$$

Conclusion

In this article, we solved the linear equation $8x - 5(x - 3) = 18$ using algebraic techniques. We expanded the expression $-5(x - 3)$, combined like terms, isolated the variable $x$, and finally solved for $x$. The solution to the equation is $x = 1$.

Frequently Asked Questions

• What is the solution to the equation $8x - 5(x - 3) = 18$?
• How do we simplify the equation $8x - 5(x - 3) = 18$?
• What is the value of the variable $x$ in the equation $8x - 5(x - 3) = 18$?

Step-by-Step Solution

1. Expand the expression $-5(x - 3)$ using the distributive property.
2. Combine like terms $8x$ and $-5x$ to simplify the equation.
3. Isolate the variable $x$ by subtracting $15$ from both sides of the equation.
4. Solve for $x$ by dividing both sides of the equation by $3$.

Final Answer

The final answer to the equation $8x - 5(x - 3) = 18$ is $x = 1$.

Introduction

In our previous article, we solved the linear equation $8x - 5(x - 3) = 18$ using algebraic techniques. In this article, we will answer some frequently asked questions related to solving linear equations.

Q&A

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

Q: How do I simplify a linear equation?

A: To simplify a linear equation, you need to combine like terms, expand expressions using the distributive property, and isolate the variable(s) on one side of the equation.

Q: What is the distributive property?

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

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

A: To isolate a variable in a linear equation, you need to get rid of the constant term(s) on the same side of the equation as the variable. You can do this by adding or subtracting the same value to both sides of the equation.

Q: What is the order of operations in solving linear equations?

A: The order of operations in solving linear equations 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 check my solution to a linear equation?

A: To check your solution to a linear equation, you need to plug the value of the variable back into the original equation and simplify. If the equation is true, then your solution 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 combining like terms
• Not using the distributive property to expand expressions
• Not isolating the variable on one side of the equation
• Not checking the solution to the equation

Conclusion

In this article, we answered some frequently asked questions related to solving linear equations. We covered topics such as simplifying linear equations, using the distributive property, isolating variables, and checking solutions. By following these tips and avoiding common mistakes, you can become proficient in solving linear equations.

Additional Resources

• For more information on solving linear equations, check out our previous article on the topic.
• For practice problems and exercises, try using online resources such as Khan Academy or Mathway.
• For more advanced topics in algebra, check out our articles on quadratic equations and systems of equations.

Final Answer

The final answer to the question "What is the solution to the equation $8x - 5(x - 3) = 18$?" is $x = 1$.