Solve For { X $} . . . { -3x + 2 = -13 \} { X = $}$ [Type Your Answer]

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Introduction

Linear equations are a fundamental concept in mathematics, and solving them is a crucial skill for students to master. In this article, we will focus on solving a specific type of linear equation, namely the equation −3x+2=−13-3x + 2 = -13. We will break down the solution process into manageable steps, making it easy for readers to understand and follow along.

What are Linear Equations?

A linear equation is an equation in which the highest power of the variable(s) is 1. In other words, it is an equation that can be written in the form ax+b=cax + b = c, where aa, bb, and cc are constants, and xx is the variable. Linear equations can be solved using various methods, including algebraic manipulation, graphing, and substitution.

The Equation −3x+2=−13-3x + 2 = -13

The equation we will be solving is −3x+2=−13-3x + 2 = -13. This equation is a linear equation in one variable, xx. Our goal is to isolate the variable xx and find its value.

Step 1: Subtract 2 from Both Sides

To begin solving the equation, we need to isolate the term containing the variable, xx. The first step is to subtract 2 from both sides of the equation. This will eliminate the constant term on the left-hand side.

-3x + 2 - 2 = -13 - 2

Simplifying the equation, we get:

-3x = -15

Step 2: Divide Both Sides by -3

Now that we have isolated the term containing the variable, we need to get rid of the coefficient, −3-3. We can do this by dividing both sides of the equation by −3-3.

\frac{-3x}{-3} = \frac{-15}{-3}

Simplifying the equation, we get:

x = 5

Conclusion

In this article, we solved the linear equation −3x+2=−13-3x + 2 = -13 using algebraic manipulation. We broke down the solution process into manageable steps, making it easy for readers to understand and follow along. By isolating the variable xx and eliminating the constant term, we were able to find the value of xx, which is 55.

Tips and Tricks

When solving linear equations, it's essential to follow the order of operations (PEMDAS):

  1. Parentheses: Evaluate expressions inside parentheses first.
  2. Exponents: Evaluate any exponential expressions next.
  3. Multiplication and Division: Evaluate multiplication and division operations from left to right.
  4. Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

Additionally, when solving linear equations, it's crucial to check your work by plugging the solution back into the original equation. This will help you verify that your solution is correct.

Common Mistakes to Avoid

When solving linear equations, there are several common mistakes to avoid:

  1. Not following the order of operations: Failing to follow the order of operations can lead to incorrect solutions.
  2. Not isolating the variable: Failing to isolate the variable can make it difficult to solve the equation.
  3. Not checking your work: Failing to check your work can lead to incorrect solutions.

By avoiding these common mistakes and following the steps outlined in this article, you'll be well on your way to becoming proficient in solving linear equations.

Final Thoughts

Solving linear equations is a fundamental skill in mathematics, and it's essential to master it. By following the steps outlined in this article and avoiding common mistakes, you'll be able to solve linear equations with ease. Remember to always check your work and verify your solutions to ensure accuracy. With practice and patience, you'll become proficient in solving linear equations and be able to tackle more complex mathematical problems with confidence.

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Introduction

In our previous article, we explored the concept of solving linear equations and walked through a step-by-step solution to the equation −3x+2=−13-3x + 2 = -13. In this article, we will address some of the most frequently asked questions about 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. In other words, it is an equation that can be written in the form ax+b=cax + b = c, where aa, bb, and cc are constants, and xx is the variable.

Q: How do I know if an equation is linear?

A: To determine if an equation is linear, look for the following characteristics:

  • The highest power of the variable(s) is 1.
  • The equation can be written in the form ax+b=cax + b = c.
  • The equation does not contain any exponential or trigonometric functions.

Q: What are some common types of linear equations?

A: Some common types of linear equations include:

  • Simple linear equations: Equations in the form ax+b=cax + b = c, where aa, bb, and cc are constants.
  • Linear equations with fractions: Equations in the form axb+c=d\frac{ax}{b} + c = d, where aa, bb, cc, and dd are constants.
  • Linear equations with decimals: Equations in the form ax+b=cax + b = c, where aa, bb, and cc are decimals.

Q: How do I solve a linear equation with fractions?

A: To solve a linear equation with fractions, follow these steps:

  1. Multiply both sides of the equation by the least common multiple (LCM) of the denominators.
  2. Simplify the equation.
  3. Solve for the variable.

Q: How do I solve a linear equation with decimals?

A: To solve a linear equation with decimals, follow these steps:

  1. Multiply both sides of the equation by 10 to eliminate the decimals.
  2. Simplify the equation.
  3. Solve for the variable.

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

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

  • Not following the order of operations: Failing to follow the order of operations can lead to incorrect solutions.
  • Not isolating the variable: Failing to isolate the variable can make it difficult to solve the equation.
  • Not checking your work: Failing to check your work can lead to incorrect solutions.

Q: How do I check my work when solving a linear equation?

A: To check your work when solving a linear equation, follow these steps:

  1. Plug the solution back into the original equation.
  2. Simplify the equation.
  3. Verify that the solution is correct.

Conclusion

Solving linear equations is a fundamental skill in mathematics, and it's essential to master it. By following the steps outlined in this article and avoiding common mistakes, you'll be able to solve linear equations with ease. Remember to always check your work and verify your solutions to ensure accuracy. With practice and patience, you'll become proficient in solving linear equations and be able to tackle more complex mathematical problems with confidence.

Final Thoughts

Solving linear equations is a crucial skill in mathematics, and it's essential to practice regularly to become proficient. By following the steps outlined in this article and avoiding common mistakes, you'll be able to solve linear equations with ease. Remember to always check your work and verify your solutions to ensure accuracy. With practice and patience, you'll become proficient in solving linear equations and be able to tackle more complex mathematical problems with confidence.