Solve The Equation:\[$-2m - 8 = 14\$\]a) \[$m = -11\$\]

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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 linear equation, step by step, to help readers understand the process and build their confidence in solving similar equations.

The Equation

The equation we will be solving is:

−2m−8=14-2m - 8 = 14

This is a linear equation in one variable, where the variable is mm. Our goal is to isolate the variable mm and find its value.

Step 1: Add 8 to Both Sides

To start solving the equation, we need to get rid of the negative term on the left-hand side. We can do this by adding 8 to both sides of the equation. This will cancel out the -8 on the left-hand side and leave us with:

−2m=22-2m = 22

Step 2: Divide Both Sides by -2

Now that we have the equation in the form −2m=22-2m = 22, we need to isolate the variable mm. We can do this by dividing both sides of the equation by -2. This will give us:

m=−222m = -\frac{22}{2}

Step 3: Simplify the Fraction

The fraction −222-\frac{22}{2} can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 2. This gives us:

m=−11m = -11

Conclusion

And there you have it! The solution to the equation −2m−8=14-2m - 8 = 14 is m=−11m = -11. This is a simple linear equation, but it requires careful attention to detail and a step-by-step approach to solve.

Why is Solving Linear Equations Important?

Solving linear equations is an essential skill in mathematics, and it has many real-world applications. For example, in physics, linear equations are used to describe the motion of objects, while in economics, they are used to model the behavior of markets. In computer science, linear equations are used to solve systems of equations and optimize algorithms.

Tips and Tricks for Solving Linear Equations

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

  • Read the equation carefully: Before starting to solve the equation, read it carefully to understand what it's asking for.
  • Use inverse operations: To isolate the variable, use inverse operations such as addition, subtraction, multiplication, and division.
  • Check your work: Once you think you have the solution, check your work by plugging the value back into the original equation.
  • Practice, practice, practice: The more you practice solving linear equations, the more comfortable you'll become with the process.

Common Mistakes to Avoid

Here are some common mistakes to avoid when solving linear equations:

  • Not reading the equation carefully: Failing to read the equation carefully can lead to mistakes in solving the equation.
  • Not using inverse operations: Failing to use inverse operations can lead to incorrect solutions.
  • Not checking your work: Failing to check your work can lead to incorrect solutions.
  • Not practicing enough: Failing to practice enough can lead to a lack of confidence in solving linear equations.

Conclusion

Introduction

In our previous article, we covered the basics of solving linear equations, including a step-by-step guide to solving the equation −2m−8=14-2m - 8 = 14. In this article, we will answer some common questions that students often have when it comes 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 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 or not?

A: To determine if an equation is linear or not, look for the highest power of the variable. If the highest power is 1, then the equation is linear. If the highest power is greater than 1, then the equation is not linear.

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. For example, the equation x+2=5x + 2 = 5 is a linear equation, while the equation x2+2x+1=0x^2 + 2x + 1 = 0 is a quadratic equation.

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 by canceling out any common factors.
  3. Solve the equation using the steps outlined in our previous article.

Q: What is the order of operations when solving a linear equation?

A: When solving a linear equation, follow the order of operations (PEMDAS):

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

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 value back into the original equation.
  2. Simplify the equation to see if it is true.
  3. 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 reading the equation carefully.
  • Not using inverse operations.
  • Not checking your work.
  • Not practicing enough.

Conclusion

Solving linear equations is a crucial skill in mathematics, and it has many real-world applications. By following the step-by-step guide outlined in this article, you can master the process of solving linear equations and build your confidence in solving similar equations. Remember to read the equation carefully, use inverse operations, check your work, and practice, practice, practice!

Additional Resources

For more information on solving linear equations, check out the following resources:

  • Khan Academy: Linear Equations
  • Mathway: Linear Equations
  • Wolfram Alpha: Linear Equations

Practice Problems

Try solving the following linear equations:

  1. 2x+3=72x + 3 = 7
  2. x−2=5x - 2 = 5
  3. 3x+2=113x + 2 = 11

Answer Key

  1. x=2x = 2
  2. x=7x = 7
  3. x=3x = 3