Solve $13 = 3x - 5$.

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Introduction

In this article, we will focus on solving a linear equation, which is a fundamental concept in mathematics. A linear equation is an equation in which the highest power of the variable(s) is 1. The equation we will be solving is $13 = 3x - 5$. This equation is a simple linear equation, and we will use basic algebraic techniques to solve it.

Understanding the Equation

Before we start solving the equation, let's understand what it means. The equation $13 = 3x - 5$ states that the value of 13 is equal to 3 times a variable x minus 5. Our goal is to find the value of x that satisfies this equation.

Isolating the Variable

To solve the equation, we need to isolate the variable x. This means we need to get x by itself on one side of the equation. We can do this by adding or subtracting the same value to both sides of the equation.

Step 1: Add 5 to Both Sides

Let's start by adding 5 to both sides of the equation. This will help us get rid of the negative term on the right-hand side.

13=3x−513 = 3x - 5

Add 5 to both sides:

13+5=3x−5+513 + 5 = 3x - 5 + 5

Simplify:

18=3x18 = 3x

Step 2: Divide Both Sides by 3

Now that we have isolated the term with x, we can divide both sides of the equation by 3 to find the value of x.

18=3x18 = 3x

Divide both sides by 3:

183=3x3\frac{18}{3} = \frac{3x}{3}

Simplify:

6=x6 = x

Conclusion

We have successfully solved the linear equation $13 = 3x - 5$. By following the steps outlined above, we were able to isolate the variable x and find its value. The final answer is x = 6.

Example Use Case

Solving linear equations is a fundamental skill in mathematics, and it has many practical applications in real-life situations. For example, in finance, linear equations can be used to calculate interest rates, investment returns, and other financial metrics. In science, linear equations can be used to model population growth, chemical reactions, and other physical phenomena.

Tips and Tricks

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

  • Always start by isolating the variable x.
  • Use basic algebraic operations such as addition, subtraction, multiplication, and division to simplify the equation.
  • Be careful when dividing both sides of the equation by a fraction.
  • Check your answer by plugging it back into the original equation.

Common Mistakes

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

  • Not isolating the variable x.
  • Not simplifying the equation properly.
  • Dividing both sides of the equation by a fraction without checking the result.
  • Not checking the answer by plugging it back into the original equation.

Final Thoughts

Solving linear equations is a fundamental skill in mathematics, and it has many practical applications in real-life situations. By following the steps outlined above and avoiding common mistakes, you can become proficient in solving linear equations and apply this skill to a wide range of problems.

Additional Resources

If you want to learn more about solving linear equations, here are some additional resources:

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

Frequently Asked Questions

Here are some frequently asked questions about solving linear equations:

  • Q: What is a linear equation? A: A linear equation is an equation in which the highest power of the variable(s) is 1.
  • Q: How do I solve a linear equation? A: To solve a linear equation, you need to isolate the variable x by using basic algebraic operations such as addition, subtraction, multiplication, and division.
  • Q: What are some common mistakes to avoid when solving linear equations? A: Some common mistakes to avoid when solving linear equations include not isolating the variable x, not simplifying the equation properly, dividing both sides of the equation by a fraction without checking the result, and not checking the answer by plugging it back into the original equation.

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Q&A: Solving Linear Equations

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 fundamental concept in mathematics and has many practical applications in real-life situations.

Q: How do I solve a linear equation?

A: To solve a linear equation, you need to isolate the variable x by using basic algebraic operations such as addition, subtraction, multiplication, and division. Here are the steps to follow:

  1. Simplify the equation by combining like terms.
  2. Add or subtract the same value to both sides of the equation to isolate the variable x.
  3. Multiply or divide both sides of the equation by a coefficient to isolate the variable x.
  4. Check your answer by plugging it back into the original equation.

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

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

  • Not isolating the variable x.
  • Not simplifying the equation properly.
  • Dividing both sides of the equation by a fraction without checking the result.
  • Not checking the answer by plugging it back into the original equation.

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

A: To check your answer when solving a linear equation, plug the value of x back into the original equation and simplify. If the equation is true, then your answer is correct.

Q: What are some real-life applications of solving linear equations?

A: Solving linear equations has many practical applications in real-life situations, including:

  • Finance: Linear equations can be used to calculate interest rates, investment returns, and other financial metrics.
  • Science: Linear equations can be used to model population growth, chemical reactions, and other physical phenomena.
  • Engineering: Linear equations can be used to design and optimize systems, such as bridges, buildings, and electronic circuits.

Q: How do I use technology to solve linear equations?

A: There are many online tools and software programs that can help you solve linear equations, including:

  • Graphing calculators: These can be used to visualize and solve linear equations.
  • Online equation solvers: These can be used to solve linear equations and other types of equations.
  • Computer algebra systems: These can be used to solve linear equations and other types of equations, as well as to perform other mathematical operations.

Q: What are some tips for solving linear equations?

A: Here are some tips for solving linear equations:

  • Always start by simplifying the equation.
  • Use basic algebraic operations such as addition, subtraction, multiplication, and division to isolate the variable x.
  • Be careful when dividing both sides of the equation by a fraction.
  • Check your answer by plugging it back into the original equation.

Q: How do I teach others to solve linear equations?

A: Here are some tips for teaching others to solve linear equations:

  • Start with simple examples and gradually move on to more complex ones.
  • Use visual aids such as graphs and charts to help students understand the concept.
  • Provide step-by-step instructions and examples to help students follow along.
  • Encourage students to practice solving linear equations on their own.

Conclusion

Solving linear equations is a fundamental skill in mathematics, and it has many practical applications in real-life situations. By following the steps outlined above and avoiding common mistakes, you can become proficient in solving linear equations and apply this skill to a wide range of problems.