Solve The Equation For \[$ Y \$\]:$\[ 3 + 6y = 15 \\]

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Understanding Linear Equations

Linear equations are a fundamental concept in mathematics, and they play a crucial role in various fields, including algebra, geometry, and calculus. 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 = c, where a, b, and c are constants, and x is the variable.

The Equation to be Solved

The equation to be solved is 3 + 6y = 15. This is a linear equation in one variable, y. Our goal is to isolate y and find its value.

Step 1: Subtract 3 from Both Sides

To solve for y, we need to isolate y on one side of the equation. The first step is to subtract 3 from both sides of the equation. This will help us get rid of the constant term on the left-hand side.

3 + 6y = 15
3 + 6y - 3 = 15 - 3
6y = 12

Step 2: Divide Both Sides by 6

Now that we have 6y on the left-hand side, we need to get rid of the coefficient 6. We can do this by dividing both sides of the equation by 6.

6y = 12
y = 12 / 6
y = 2

The Final Answer

Therefore, the value of y is 2. This is the solution to the equation 3 + 6y = 15.

Why is Solving Linear Equations Important?

Solving linear equations is an essential skill in mathematics, and it has numerous applications in real-life situations. Here are a few examples:

  • Physics and Engineering: Linear equations are used to describe the motion of objects, the flow of fluids, and the behavior of electrical circuits.
  • Economics: Linear equations are used to model the behavior of economic systems, including supply and demand curves.
  • Computer Science: Linear equations are used in computer graphics, game development, and machine learning.

Tips and Tricks for Solving Linear Equations

Here are a few tips and tricks for solving linear equations:

  • Use the Order of Operations: When solving linear equations, it's essential to follow the order of operations (PEMDAS): Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction.
  • Isolate the Variable: To solve for a variable, you need to isolate it on one side of the equation. This can be done by adding, subtracting, multiplying, or dividing both sides of the equation by the same value.
  • Check Your Work: Once you've solved for the variable, it's essential to check your work by plugging the solution back into the original equation.

Conclusion

Solving linear equations is a fundamental skill in mathematics, and it has numerous applications in real-life situations. By following the steps outlined in this article, you can solve linear equations with ease. Remember to use the order of operations, isolate the variable, and check your work to ensure that your solution is correct.

Frequently Asked Questions

Here are a few 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 on one side of the equation. This can be done by adding, subtracting, multiplying, or dividing both sides of the equation by the same value.
  • Q: What are some common mistakes to avoid when solving linear equations? A: Some common mistakes to avoid when solving linear equations include forgetting to use the order of operations, not isolating the variable, and not checking your work.

Additional Resources

Here are a few additional resources for learning more about solving linear equations:

  • Online Tutorials: There are many online tutorials and videos that can help you learn how to solve linear equations.
  • Math Books: There are many math books that can provide you with a comprehensive understanding of linear equations and how to solve them.
  • Practice Problems: Practice problems are an excellent way to reinforce your understanding of linear equations and improve your problem-solving skills.

Final Thoughts

Solving linear equations is a fundamental skill in mathematics, and it has numerous applications in real-life situations. By following the steps outlined in this article, you can solve linear equations with ease. Remember to use the order of operations, isolate the variable, and check your work to ensure that your solution is correct. With practice and patience, you can become proficient in solving linear equations and tackle more complex math problems with confidence.

Understanding Linear Equations

Linear equations are a fundamental concept in mathematics, and they play a crucial role in various fields, including algebra, geometry, and calculus. 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 = c, where a, b, and c are constants, and x is the variable.

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.

Q: How do I solve a linear equation?

A: To solve a linear equation, you need to isolate the variable on one side of the equation. This can be done by adding, subtracting, multiplying, or dividing both sides of the equation by the same value.

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

A: Some common mistakes to avoid when solving linear equations include forgetting to use the order of operations, not isolating the variable, and not checking your work.

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

A: To check your work, plug the solution back into the original equation and verify that it is true.

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(s) is 1, while a quadratic equation is an equation in which the highest power of the variable(s) is 2.

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 steps involved in solving the equation and to check your work to ensure that the solution is correct.

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

A: To solve a linear equation with fractions, multiply both sides of the equation by the least common multiple (LCM) of the denominators to eliminate the fractions.

Q: Can I solve a linear equation with variables on both sides?

A: Yes, you can solve a linear equation with variables on both sides by isolating one variable and then solving for the other variable.

Q: How do I solve a linear equation with a negative coefficient?

A: To solve a linear equation with a negative coefficient, multiply both sides of the equation by -1 to eliminate the negative sign.

Q: Can I use algebraic properties to solve linear equations?

A: Yes, you can use algebraic properties, such as the distributive property and the commutative property, to solve linear equations.

Tips and Tricks for Solving Linear Equations

Here are a few tips and tricks for solving linear equations:

  • Use the Order of Operations: When solving linear equations, it's essential to follow the order of operations (PEMDAS): Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction.
  • Isolate the Variable: To solve for a variable, you need to isolate it on one side of the equation. This can be done by adding, subtracting, multiplying, or dividing both sides of the equation by the same value.
  • Check Your Work: Once you've solved for the variable, it's essential to check your work by plugging the solution back into the original equation.

Conclusion

Solving linear equations is a fundamental skill in mathematics, and it has numerous applications in real-life situations. By following the steps outlined in this article, you can solve linear equations with ease. Remember to use the order of operations, isolate the variable, and check your work to ensure that your solution is correct.

Frequently Asked Questions

Here are a few 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 on one side of the equation. This can be done by adding, subtracting, multiplying, or dividing both sides of the equation by the same value.
  • Q: What are some common mistakes to avoid when solving linear equations? A: Some common mistakes to avoid when solving linear equations include forgetting to use the order of operations, not isolating the variable, and not checking your work.

Additional Resources

Here are a few additional resources for learning more about solving linear equations:

  • Online Tutorials: There are many online tutorials and videos that can help you learn how to solve linear equations.
  • Math Books: There are many math books that can provide you with a comprehensive understanding of linear equations and how to solve them.
  • Practice Problems: Practice problems are an excellent way to reinforce your understanding of linear equations and improve your problem-solving skills.

Final Thoughts

Solving linear equations is a fundamental skill in mathematics, and it has numerous applications in real-life situations. By following the steps outlined in this article, you can solve linear equations with ease. Remember to use the order of operations, isolate the variable, and check your work to ensure that your solution is correct. With practice and patience, you can become proficient in solving linear equations and tackle more complex math problems with confidence.