Solve The Equation S − 12 = 20 S - 12 = 20 S − 12 = 20 . S = S = S =

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 simple linear equation, $s - 12 = 20$, to understand the step-by-step process involved. By the end of this article, you will be able to solve similar equations with ease.

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 $ax + b = c$, where $a$, $b$, and $c$ are constants, and $x$ is the variable. Linear equations can be solved using various methods, including algebraic manipulation and graphical representation.

The Equation $s - 12 = 20$

The given equation is $s - 12 = 20$. To solve for $s$, we need to isolate the variable $s$ on one side of the equation. This can be done by adding 12 to both sides of the equation.

Step 1: Add 12 to Both Sides

When we add 12 to both sides of the equation, we get:

$s - 12 + 12 = 20 + 12$

This simplifies to:

$s = 32$

Understanding the Solution

In the previous step, we added 12 to both sides of the equation to isolate the variable $s$. This is a common technique used to solve linear equations. By adding or subtracting the same value from both sides of the equation, we can move the constant term to the other side, leaving the variable term alone.

Why Does This Work?

When we add 12 to both sides of the equation, we are essentially "cancelling out" the -12 on the left side. This is because -12 + 12 = 0, which means that the -12 term is eliminated. As a result, the variable $s$ is left alone on the left side, and the constant term 20 is left alone on the right side.

Real-World Applications

Solving linear equations has numerous real-world applications. For example, in finance, linear equations can be used to calculate interest rates, investment returns, and loan payments. In science, linear equations can be used to model population growth, chemical reactions, and physical systems.

Conclusion

In this article, we solved the linear equation $s - 12 = 20$ using the step-by-step process of adding 12 to both sides of the equation. By understanding the concept of linear equations and how to solve them, you can apply this skill to a wide range of real-world problems. Whether you're a student, a professional, or simply someone interested in mathematics, solving linear equations is an essential skill to master.

Additional Resources

For further practice and review, here are some additional resources:

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

Frequently Asked Questions

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 can use algebraic manipulation, such as adding or subtracting the same value from both sides of the equation.

Introduction

In our previous article, we solved the linear equation $s - 12 = 20$ using the step-by-step process of adding 12 to both sides of the equation. In this article, we will continue to explore the concept of linear equations and answer some frequently asked questions.

Q&A Session

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 $ax + b = c$, 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 can use algebraic manipulation, such as adding or subtracting the same value from both sides of the equation. For example, if you have the equation $x + 3 = 7$, you can subtract 3 from both sides to get $x = 4$.

Q: What are some common types of linear equations?

A: There are several types of linear equations, including:

• Simple linear equations: These are equations in which the variable is isolated on one side of the equation. For example, $x + 2 = 5$.
• Linear equations with fractions: These are equations in which the variable is multiplied or divided by a fraction. For example, $\frac{x}{2} + 1 = 3$.
• Linear equations with decimals: These are equations in which the variable is multiplied or divided by a decimal. For example, $x + 0.5 = 2.5$.

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

A: To solve a linear equation with fractions, you can multiply both sides of the equation by the denominator of the fraction. For example, if you have the equation $\frac{x}{2} + 1 = 3$, you can multiply both sides by 2 to get $x + 2 = 6$.

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

A: To solve a linear equation with decimals, you can multiply both sides of the equation by 10 to get rid of the decimal. For example, if you have the equation $x + 0.5 = 2.5$, you can multiply both sides by 10 to get $10x + 5 = 25$.

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

A: Linear equations have numerous real-world applications, including:

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

Q: How do I graph a linear equation?

A: To graph a linear equation, you can use the slope-intercept form of the equation, which is $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept. You can plot the y-intercept on the y-axis and then use the slope to find the x-intercept.

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. For example, $x + 2 = 5$ is a linear equation, while $x^2 + 4x + 4 = 0$ is a quadratic equation.

Conclusion

In this article, we answered some frequently asked questions about linear equations, including how to solve them, common types of linear equations, and real-world applications. We also discussed how to graph a linear equation and the difference between a linear equation and a quadratic equation. Whether you're a student, a professional, or simply someone interested in mathematics, understanding linear equations is an essential skill to master.

Additional Resources

For further practice and review, here are some additional resources:

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

Frequently Asked Questions

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 can use algebraic manipulation, such as adding or subtracting the same value from both sides of the equation.

Q: What are some real-world applications of linear equations? A: Linear equations have numerous real-world applications, including finance, science, and engineering.