Solve The Following Equation:${-5x - 5 = 25}$

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Introduction

Linear equations are a fundamental concept in mathematics, and solving them is a crucial skill for students and professionals alike. In this article, we will focus on solving a specific linear equation, step by step, and provide a comprehensive guide on how to approach similar problems.

What is a Linear Equation?

A linear equation is an equation in which the highest power of the variable(s) is 1. It can be written in the form of ax + b = c, where a, b, and c are constants, and x is the variable. Linear equations can be solved using various methods, including algebraic manipulation, graphing, and substitution.

The Given Equation

The given equation is:

-5x - 5 = 25

Step 1: Add 5 to Both Sides

To isolate the term with the variable, we need to get rid of the constant term on the same side as the variable. In this case, we can add 5 to both sides of the equation to get:

-5x = 25 + 5

Step 2: Simplify the Right Side

Now, we can simplify the right side of the equation by adding 25 and 5:

-5x = 30

Step 3: Divide Both Sides by -5

To solve for x, we need to get rid of the coefficient of x, which is -5. We can do this by dividing both sides of the equation by -5:

x = -30 / -5

Step 4: Simplify the Right Side

Now, we can simplify the right side of the equation by dividing -30 by -5:

x = 6

Conclusion

In this article, we solved a linear equation step by step, using algebraic manipulation. We added 5 to both sides of the equation to isolate the term with the variable, simplified the right side, and finally divided both sides by -5 to solve for x. This problem-solving approach can be applied to similar linear equations, and with practice, you will become proficient in solving them.

Tips and Tricks

  • When solving linear equations, always start by isolating the term with the variable.
  • Use inverse operations to get rid of the coefficient of the variable.
  • Simplify the right side of the equation as you go along.
  • Check your solution by plugging it back into the original equation.

Real-World Applications

Linear equations have numerous real-world applications, including:

  • Physics: Linear equations are used to describe the motion of objects under constant acceleration.
  • Engineering: Linear equations are used to design and optimize systems, such as electrical circuits and mechanical systems.
  • Economics: Linear equations are used to model economic systems and make predictions about future trends.

Common Mistakes to Avoid

When solving linear equations, it's essential to avoid common mistakes, such as:

  • Not isolating the term with the variable.
  • Not using inverse operations to get rid of the coefficient of the variable.
  • Not simplifying the right side of the equation as you go along.

Practice Problems

To reinforce your understanding of solving linear equations, try the following practice problems:

  • Solve the equation: 2x + 3 = 7
  • Solve the equation: x - 2 = 9
  • Solve the equation: 4x = 24

Conclusion

Solving linear equations is a fundamental skill that has numerous real-world applications. By following the step-by-step guide provided in this article, you will become proficient in solving linear equations and be able to apply this skill to various problems. Remember to avoid common mistakes and practice regularly to reinforce your understanding.

Final Thoughts

Linear equations are a crucial concept in mathematics, and solving them is a vital skill for students and professionals alike. By mastering the art of solving linear equations, you will be able to tackle complex problems and make informed decisions in various fields. So, keep practicing, and soon you will become a pro at solving linear equations!

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Introduction

In our previous article, we provided a step-by-step guide on solving linear equations. However, we understand that sometimes, it's easier to learn through questions and answers. In this article, we will address some common questions and provide answers to help you better understand how to solve 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 can be written in the form of ax + b = c, where a, b, and c are constants, and x is the variable.

Q: How do I solve a linear equation?

A: To solve a linear equation, you need to isolate the term with the variable. You can do this by using inverse operations, such as addition, subtraction, multiplication, and division.

Q: What is the difference between a linear equation and a quadratic equation?

A: A linear equation has the highest power of the variable as 1, while a quadratic equation has the highest power of the variable as 2. For example, 2x + 3 = 7 is a linear equation, while x^2 + 4x + 4 = 0 is a quadratic equation.

Q: Can I use a calculator to solve linear equations?

A: Yes, you can use a calculator to solve linear equations. However, it's essential to understand the concept behind solving linear equations, as calculators can only provide the solution, not the process.

Q: How do I check my solution?

A: To check your solution, plug it back into the original equation and verify that it's true. For example, if you solved the equation 2x + 3 = 7 and got x = 2, plug x = 2 back into the equation to verify that it's true: 2(2) + 3 = 7.

Q: What if I have a fraction or decimal coefficient?

A: If you have a fraction or decimal coefficient, you can multiply both sides of the equation by the reciprocal of the coefficient to eliminate it. For example, if you have the equation 1/2x = 3, you can multiply both sides by 2 to get x = 6.

Q: Can I solve linear equations with multiple variables?

A: Yes, you can solve linear equations with multiple variables. However, it's essential to understand that each variable must be isolated separately, and you may need to use substitution or elimination methods to solve the equation.

Q: What if I have a linear equation with a negative coefficient?

A: If you have a linear equation with a negative coefficient, you can multiply both sides of the equation by -1 to eliminate the negative sign. For example, if you have the equation -2x = 6, you can multiply both sides by -1 to get 2x = -6.

Conclusion

Solving linear equations is a fundamental skill that has numerous real-world applications. By understanding the concept behind solving linear equations and practicing regularly, you will become proficient in solving linear equations and be able to apply this skill to various problems. Remember to check your solution and avoid common mistakes.

Final Thoughts

Linear equations are a crucial concept in mathematics, and solving them is a vital skill for students and professionals alike. By mastering the art of solving linear equations, you will be able to tackle complex problems and make informed decisions in various fields. So, keep practicing, and soon you will become a pro at solving linear equations!

Practice Problems

To reinforce your understanding of solving linear equations, try the following practice problems:

  • Solve the equation: 2x + 3 = 7
  • Solve the equation: x - 2 = 9
  • Solve the equation: 4x = 24
  • Solve the equation: 1/2x = 3
  • Solve the equation: -2x = 6

Resources

For further learning and practice, we recommend the following resources:

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

Conclusion

Solving linear equations is a fundamental skill that has numerous real-world applications. By understanding the concept behind solving linear equations and practicing regularly, you will become proficient in solving linear equations and be able to apply this skill to various problems. Remember to check your solution and avoid common mistakes.