Solve The Equation:${ 3(-5x - 3) = -10x - (x - 6) }$

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Introduction

In mathematics, equations are a fundamental concept that helps us understand the relationship between variables and constants. Solving equations is a crucial skill that is used in various fields, including physics, engineering, and economics. In this article, we will focus on solving a specific equation, which involves simplifying and isolating the variable. We will break down the solution into manageable steps, making it easier for readers to understand and follow along.

The Given Equation

The given equation is:

3(βˆ’5xβˆ’3)=βˆ’10xβˆ’(xβˆ’6){ 3(-5x - 3) = -10x - (x - 6) }

This equation involves parentheses, which need to be simplified before we can proceed with solving for the variable. Let's start by simplifying the left-hand side of the equation.

Simplifying the Left-Hand Side

To simplify the left-hand side, we need to distribute the 3 to the terms inside the parentheses.

3(βˆ’5xβˆ’3)=βˆ’15xβˆ’9{ 3(-5x - 3) = -15x - 9 }

Now, the equation becomes:

βˆ’15xβˆ’9=βˆ’10xβˆ’(xβˆ’6){ -15x - 9 = -10x - (x - 6) }

Simplifying the Right-Hand Side

Next, we need to simplify the right-hand side of the equation. To do this, we need to distribute the negative sign to the terms inside the parentheses.

βˆ’10xβˆ’(xβˆ’6)=βˆ’10xβˆ’x+6{ -10x - (x - 6) = -10x - x + 6 }

Simplifying further, we get:

βˆ’10xβˆ’x+6=βˆ’11x+6{ -10x - x + 6 = -11x + 6 }

Now, the equation becomes:

βˆ’15xβˆ’9=βˆ’11x+6{ -15x - 9 = -11x + 6 }

Isolating the Variable

To isolate the variable, we need to get all the terms involving x on one side of the equation. Let's start by adding 11x to both sides of the equation.

βˆ’15x+11xβˆ’9=βˆ’11x+11x+6{ -15x + 11x - 9 = -11x + 11x + 6 }

Simplifying further, we get:

βˆ’4xβˆ’9=6{ -4x - 9 = 6 }

Next, we need to add 9 to both sides of the equation.

βˆ’4xβˆ’9+9=6+9{ -4x - 9 + 9 = 6 + 9 }

Simplifying further, we get:

βˆ’4x=15{ -4x = 15 }

Solving for x

To solve for x, we need to isolate x by dividing both sides of the equation by -4.

βˆ’4xβˆ’4=15βˆ’4{ \frac{-4x}{-4} = \frac{15}{-4} }

Simplifying further, we get:

x=βˆ’154{ x = -\frac{15}{4} }

Conclusion

In this article, we solved the equation 3(-5x - 3) = -10x - (x - 6) by simplifying and isolating the variable. We broke down the solution into manageable steps, making it easier for readers to understand and follow along. By following these steps, readers can solve similar equations and develop a deeper understanding of algebraic manipulations.

Frequently Asked Questions

Q: What is the value of x in the equation 3(-5x - 3) = -10x - (x - 6)?

A: The value of x is -15/4.

Q: How do I simplify the left-hand side of the equation?

A: To simplify the left-hand side, you need to distribute the 3 to the terms inside the parentheses.

Q: How do I simplify the right-hand side of the equation?

A: To simplify the right-hand side, you need to distribute the negative sign to the terms inside the parentheses.

Q: How do I isolate the variable?

A: To isolate the variable, you need to get all the terms involving x on one side of the equation.

Final Answer

The final answer is: βˆ’154\boxed{-\frac{15}{4}}

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Introduction

In our previous article, we solved the equation 3(-5x - 3) = -10x - (x - 6) by simplifying and isolating the variable. In this article, we will provide a Q&A guide to help readers understand and apply the concepts learned in the previous article.

Q&A

Q: What is the first step in solving an equation?

A: The first step in solving an equation is to simplify the equation by removing any parentheses or brackets.

Q: How do I simplify an equation with parentheses?

A: To simplify an equation with parentheses, you need to distribute the terms inside the parentheses to the terms outside 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 linear equation?

A: To solve a linear equation, you need to isolate the variable by adding, subtracting, multiplying, or dividing both sides of the equation by the same value.

Q: What is the order of operations in solving an equation?

A: The order of operations in solving an equation is:

  1. Parentheses: Simplify any expressions inside parentheses.
  2. Exponents: Simplify any exponential expressions.
  3. Multiplication and Division: Simplify any multiplication and division operations from left to right.
  4. Addition and Subtraction: Simplify any addition and subtraction operations from left to right.

Q: How do I check my solution to an equation?

A: To check your solution to an equation, you need to substitute the value of the variable back into the original equation and simplify.

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

A: Some common mistakes to avoid when solving equations include:

  • Not simplifying the equation before solving
  • Not isolating the variable
  • Not checking the solution
  • Not using the correct order of operations

Tips and Tricks

Tip 1: Simplify the equation before solving

Simplifying the equation before solving can make it easier to isolate the variable and find the solution.

Tip 2: Use the correct order of operations

Using the correct order of operations can help you avoid mistakes and ensure that you are solving the equation correctly.

Tip 3: Check your solution

Checking your solution can help you ensure that you have found the correct value of the variable.

Conclusion

In this article, we provided a Q&A guide to help readers understand and apply the concepts learned in our previous article on solving equations. We covered topics such as simplifying equations, solving linear equations, and checking solutions. By following these tips and tricks, readers can improve their skills in solving equations and become more confident in their math abilities.

Frequently Asked Questions

Q: What is the best way to simplify an equation?

A: The best way to simplify an equation is to remove any parentheses or brackets and then use the correct order of operations.

Q: How do I know if I have found the correct solution to an equation?

A: You can check your solution by substituting the value of the variable back into the original equation and simplifying.

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

A: Some common mistakes to avoid when solving equations include not simplifying the equation before solving, not isolating the variable, and not checking the solution.

Final Answer

The final answer is: There is no final answer, as this article is a Q&A guide to help readers understand and apply the concepts learned in our previous article on solving equations.