Solve For \[$ S \$\]:$\[ S + 159 = 25 \\]
Introduction
Linear equations are a fundamental concept in mathematics, and solving them is a crucial skill for students and professionals alike. In this article, we will focus on solving a simple linear equation, step by step, to help you understand the process and build your confidence in tackling more complex equations.
What is a Linear Equation?
A linear equation is an equation in which the highest power of the variable (usually x) is 1. It can be written in the form:
ax + b = c
where a, b, and c are constants, and x is the variable.
The Equation to Solve
The equation we will be solving is:
s + 159 = 25
Step 1: Understand the Equation
The first step in solving a linear equation is to understand what the equation is asking. In this case, we are looking for the value of s, which is the variable.
Step 2: Isolate the Variable
To isolate the variable, we need to get rid of the constant term (159) on the same side of the equation as the variable. We can do this by subtracting 159 from both sides of the equation.
s + 159 - 159 = 25 - 159
Step 3: Simplify the Equation
Now that we have isolated the variable, we can simplify the equation by combining like terms.
s = -134
Step 4: Check the Solution
To make sure our solution is correct, we can plug it back into the original equation and check if it is true.
s + 159 = 25
-134 + 159 = 25
25 = 25
Conclusion
Solving linear equations is a straightforward process that requires patience and attention to detail. By following the steps outlined in this article, you can solve simple linear equations like the one we tackled in this example. Remember to always understand the equation, isolate the variable, simplify the equation, and check the solution to ensure that your answer is correct.
Tips and Tricks
- Always read the equation carefully and understand what it is asking.
- Use inverse operations to isolate the variable.
- Simplify the equation by combining like terms.
- Check the solution by plugging it back into the original equation.
Common Mistakes to Avoid
- Not reading the equation carefully and understanding what it is asking.
- Not using inverse operations to isolate the variable.
- Not simplifying the equation by combining like terms.
- Not checking the solution by plugging it back into the original equation.
Real-World Applications
Linear equations have many real-world applications, including:
- Finance: Linear equations are used to calculate interest rates, investment returns, and other financial metrics.
- Science: Linear equations are used to model population growth, chemical reactions, and other scientific phenomena.
- Engineering: Linear equations are used to design and optimize systems, such as bridges, buildings, and electronic circuits.
Conclusion
Introduction
In our previous article, we covered the basics of solving linear equations, including understanding the equation, isolating the variable, simplifying the equation, and checking the solution. In this article, we will answer 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 (usually x) 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, follow these steps:
- Understand the equation and what it is asking.
- Isolate the variable by using inverse operations.
- Simplify the equation by combining like terms.
- Check the solution by plugging it back into the original equation.
Q: What is an inverse operation?
A: An inverse operation is an operation that "reverses" another operation. For example, addition and subtraction are inverse operations, as are multiplication and division.
Q: How do I isolate the variable?
A: To isolate the variable, use inverse operations to get rid of the constant term on the same side of the equation as the variable. For example, if the equation is:
s + 159 = 25
You can subtract 159 from both sides to isolate the variable:
s = -134
Q: What is a like term?
A: A like term is a term that has the same variable and exponent. For example, in the equation:
2x + 3x = 5
The terms 2x and 3x are like terms, as they both have the variable x and the same exponent (1).
Q: How do I simplify the equation?
A: To simplify the equation, combine like terms by adding or subtracting their coefficients. For example, in the equation:
2x + 3x = 5
You can combine the like terms by adding their coefficients:
5x = 5
Q: Why is it important to check the solution?
A: It is essential to check the solution by plugging it back into the original equation to ensure that it is correct. This helps to prevent errors and ensures that the solution is accurate.
Q: What are some common mistakes to avoid when solving linear equations?
A: Some common mistakes to avoid when solving linear equations include:
- Not reading the equation carefully and understanding what it is asking.
- Not using inverse operations to isolate the variable.
- Not simplifying the equation by combining like terms.
- Not checking the solution by plugging it back into the original equation.
Q: How do I apply linear equations to real-world problems?
A: Linear equations have many real-world applications, including:
- Finance: Linear equations are used to calculate interest rates, investment returns, and other financial metrics.
- Science: Linear equations are used to model population growth, chemical reactions, and other scientific phenomena.
- Engineering: Linear equations are used to design and optimize systems, such as bridges, buildings, and electronic circuits.
Conclusion
Solving linear equations is a fundamental skill that has many real-world applications. By following the steps outlined in this article and avoiding common mistakes, you can solve linear equations with confidence. Remember to always understand the equation, isolate the variable, simplify the equation, and check the solution to ensure that your answer is correct.