Solve For { S $} : : : { 3s = S - 2 \}

by ADMIN 39 views

Introduction

In algebra, solving for a variable is a fundamental concept that involves isolating the variable on one side of the equation. This is a crucial skill that is used extensively in various mathematical operations, including linear equations, quadratic equations, and systems of equations. In this article, we will focus on solving for the variable s in the equation 3s = s - 2.

Understanding the Equation

The given equation is 3s = s - 2. This is a linear equation, which means it can be solved using basic algebraic operations. The equation consists of two terms: 3s and s - 2. Our goal is to isolate the variable s on one side of the equation.

Isolating the Variable

To isolate the variable s, we need to get rid of the constant term -2 on the right-hand side of the equation. We can do this by adding 2 to both sides of the equation. This will cancel out the -2 on the right-hand side, leaving us with only the variable s on the left-hand side.

Step-by-Step Solution

Here's a step-by-step solution to the equation 3s = s - 2:

  1. Add 2 to both sides of the equation: This will cancel out the -2 on the right-hand side, leaving us with only the variable s on the left-hand side.

    3s = s - 2 3s + 2 = s - 2 + 2 3s + 2 = s

  2. Subtract s from both sides of the equation: This will isolate the variable s on the left-hand side.

    3s + 2 = s 3s + 2 - s = s - s 2s + 2 = 0

  3. Subtract 2 from both sides of the equation: This will get rid of the constant term 2 on the left-hand side.

    2s + 2 = 0 2s + 2 - 2 = 0 - 2 2s = -2

  4. Divide both sides of the equation by 2: This will isolate the variable s on the left-hand side.

    2s = -2 2s / 2 = -2 / 2 s = -1

Conclusion

In conclusion, solving for the variable s in the equation 3s = s - 2 involves a series of algebraic operations, including adding, subtracting, and dividing. By following the step-by-step solution outlined above, we can isolate the variable s on one side of the equation, resulting in the solution s = -1.

Frequently Asked Questions

  • What is the value of s in the equation 3s = s - 2? The value of s in the equation 3s = s - 2 is -1.
  • How do I solve for a variable in a linear equation? To solve for a variable in a linear equation, you can use basic algebraic operations, including adding, subtracting, and dividing.
  • What is the difference between a linear equation and a quadratic equation? A linear equation is an equation that can be solved using basic algebraic operations, while a quadratic equation is an equation that involves a squared variable.

Real-World Applications

Solving for a variable is a crucial skill that has numerous real-world applications. Here are a few examples:

  • Physics: In physics, solving for a variable is used to calculate the motion of objects, including velocity, acceleration, and distance.
  • Engineering: In engineering, solving for a variable is used to design and optimize systems, including electrical circuits, mechanical systems, and thermal systems.
  • Economics: In economics, solving for a variable is used to model economic systems, including supply and demand, inflation, and unemployment.

Final Thoughts

Solving for a variable is a fundamental concept in algebra that has numerous real-world applications. By following the step-by-step solution outlined above, we can isolate the variable s on one side of the equation, resulting in the solution s = -1. Whether you're a student, a professional, or simply someone who enjoys math, solving for a variable is a skill that can be applied in a variety of contexts.

Introduction

In our previous article, we explored the concept of solving for a variable in the equation 3s = s - 2. We walked through a step-by-step solution to isolate the variable s on one side of the equation, resulting in the solution s = -1. In this article, we will delve deeper into the world of solving for variables and answer some frequently asked questions.

Q&A: Solving for Variables

Q: What is the first step in solving for a variable in a linear equation?

A: The first step in solving for a variable in a linear equation is to add, subtract, multiply, or divide both sides of the equation by the same value to isolate the variable.

Q: How do I know which operation to perform first?

A: To determine which operation to perform first, look for the variable and the constant term on the same side of the equation. If the variable is on the left-hand side and the constant term is on the right-hand side, add or subtract the constant term from both sides to isolate the variable.

Q: What is the difference between adding and subtracting in solving for a variable?

A: Adding and subtracting are both used to isolate the variable in a linear equation. However, adding is used to get rid of a negative constant term, while subtracting is used to get rid of a positive constant term.

Q: Can I multiply or divide both sides of the equation by a fraction?

A: Yes, you can multiply or divide both sides of the equation by a fraction. However, be careful not to change the sign of the variable.

Q: What is the final step in solving for a variable?

A: The final step in solving for a variable is to check your solution by plugging it back into the original equation.

Q: How do I know if my solution is correct?

A: To check if your solution is correct, plug it back into the original equation and simplify. If the equation holds true, then your solution is correct.

Q: What if I have a quadratic equation with two variables?

A: If you have a quadratic equation with two variables, you can use the quadratic formula to solve for the variables.

Q: Can I use the quadratic formula to solve for a variable in a linear equation?

A: No, the quadratic formula is used to solve for the variables in a quadratic equation, not a linear equation.

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

A: A linear equation is an equation that can be solved using basic algebraic operations, while a quadratic equation is an equation that involves a squared variable.

Q: Can I use a calculator to solve for a variable?

A: Yes, you can use a calculator to solve for a variable. However, be careful not to make any mistakes when entering the equation.

Q: What if I get stuck while solving for a variable?

A: If you get stuck while solving for a variable, try breaking down the equation into smaller steps or ask for help from a teacher or tutor.

Real-World Applications

Solving for variables has numerous real-world applications, including:

  • Physics: In physics, solving for variables is used to calculate the motion of objects, including velocity, acceleration, and distance.
  • Engineering: In engineering, solving for variables is used to design and optimize systems, including electrical circuits, mechanical systems, and thermal systems.
  • Economics: In economics, solving for variables is used to model economic systems, including supply and demand, inflation, and unemployment.

Final Thoughts

Solving for variables is a fundamental concept in algebra that has numerous real-world applications. By following the step-by-step solution outlined in this article, you can isolate the variable s on one side of the equation, resulting in the solution s = -1. Whether you're a student, a professional, or simply someone who enjoys math, solving for variables is a skill that can be applied in a variety of contexts.

Additional Resources

  • Algebra textbooks: For a comprehensive guide to solving for variables, consult an algebra textbook.
  • Online resources: For additional practice and resources, visit online websites such as Khan Academy, Mathway, or Wolfram Alpha.
  • Tutors or teachers: For one-on-one help, consider hiring a tutor or teacher to guide you through the process of solving for variables.