Solve This Equation: 2 S + S + 12 = 132 2s + S + 12 = 132 2 S + S + 12 = 132 .A) S = 9 S = 9 S = 9 B) S = − 30 S = -30 S = − 30 C) S = 120 S = 120 S = 120 D) S = 40 S = 40 S = 40

Mar 10, 2025 by ADMIN 179 views

**Solving Linear Equations: A Step-by-Step Guide**

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, $2s + s + 12 = 132$ , and explore the different methods and techniques used to find the solution.

What is a Linear Equation?

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. Linear equations can be solved using various methods, including algebraic manipulation, graphing, and substitution.

The Equation to be Solved

The equation we will be solving is $2s + s + 12 = 132$ . This equation can be simplified by combining like terms, which will make it easier to solve.

Simplifying the Equation

To simplify the equation, we need to combine the like terms on the left-hand side. The like terms in this equation are the terms with the variable $s$ . We can combine these terms by adding their coefficients.

2s + s = 3s

Now, we can rewrite the equation as:

3s + 12 = 132

Subtracting 12 from Both Sides

To isolate the term with the variable $s$ , we need to get rid of the constant term on the left-hand side. We can do this by subtracting 12 from both sides of the equation.

3s = 132 - 12
3s = 120

Dividing Both Sides by 3

Now that we have isolated the term with the variable $s$ , we can solve for $s$ by dividing both sides of the equation by 3.

s = 120 / 3
s = 40

Conclusion

In this article, we solved the linear equation $2s + s + 12 = 132$ using algebraic manipulation. We simplified the equation by combining like terms, subtracted 12 from both sides to isolate the term with the variable $s$ , and finally divided both sides by 3 to solve for $s$ . The solution to the equation is $s = 40$ .

Answer Key

The correct answer is:

A) $s = 9$ is incorrect
B) $s = -30$ is incorrect
C) $s = 120$ is incorrect
D) $s = 40$ is correct

Tips and Tricks

When solving linear equations, it's essential to simplify the equation by combining like terms.
To isolate the term with the variable, subtract the constant term from both sides of the equation.
When dividing both sides of the equation by a coefficient, make sure to divide the constant term by the same coefficient.

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.

Conclusion

Introduction

In our previous article, we solved the linear equation $2s + s + 12 = 132$ using algebraic manipulation. In this article, we will provide a Q&A guide to help students understand the concepts and techniques used to solve 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. 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: How do I simplify a linear equation?

A: To simplify a linear equation, you need to combine like terms. Like terms are terms that have the same variable and exponent. For example, in the equation $2x + 3x + 4$ , the like terms are $2x$ and $3x$ . You can combine these terms by adding their coefficients.

2x + 3x = 5x

Q: How do I isolate the term with the variable?

A: To isolate the term with the variable, you need to get rid of the constant term on the same side of the equation as the variable. You can do this by subtracting the constant term from both sides of the equation.

ax + b = c
ax = c - b

Q: How do I solve for the variable?

A: To solve for the variable, you need to divide both sides of the equation by the coefficient of the variable. The coefficient is the number in front of the variable.

ax = c - b
x = (c - b) / a

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

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

Not simplifying the equation by combining like terms.
Not isolating the term with the variable.
Not solving for the variable by dividing both sides of the equation by the coefficient.
Making errors when subtracting or adding numbers.

Q: How do I check my answer?

A: To check your answer, you need to plug the solution back into the original equation and make sure it is true. If the solution is true, then you have found the correct solution.

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

A: 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.

Q: How do I use linear equations in my daily life?

A: Linear equations can be used in your daily life in a variety of ways, including:

Budgeting: Linear equations can be used to create a budget and track expenses.
Investing: Linear equations can be used to calculate returns on investment and make informed decisions.
Science: Linear equations can be used to model and analyze data in a variety of scientific fields, including physics and biology.

Conclusion

Solving linear equations is a fundamental skill that has numerous real-world applications. By mastering the techniques and methods used to solve linear equations, students can develop a deeper understanding of mathematics and its applications. In this article, we provided a Q&A guide to help students understand the concepts and techniques used to solve linear equations. We hope that this guide has been helpful and informative.