Solve The Equation For \[$ X \$\]: $\[ 15.75 - X = -10.55 \\]

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 of the form $15.75 - x = -10.55$. We will break down the solution step by step, using clear and concise language to ensure that readers understand the process.

What is a Linear Equation?

A linear equation is an equation in which the highest power of the variable (in this case, $x$) is 1. Linear equations can be written in the form $ax + b = c$, where $a$, $b$, and $c$ are constants. In our example equation, $15.75 - x = -10.55$, we can see that the highest power of $x$ is 1, making it a linear equation.

Step 1: Isolate the Variable

To solve the equation, we need to isolate the variable $x$. In this case, we can start by adding $x$ to both sides of the equation to get rid of the negative term.

15.75 - x + x = -10.55 + x

This simplifies to:

15.75 = -10.55 + x

Step 2: Add the Constant to Both Sides

Next, we need to add the constant $-10.55$ to both sides of the equation to isolate the term with $x$.

15.75 + 10.55 = -10.55 + 10.55 + x

This simplifies to:

26.30 = x

Step 3: Check the Solution

To ensure that our solution is correct, we can plug it back into the original equation.

15.75 - 26.30 = -10.55

This simplifies to:

-10.55 = -10.55

Since the left-hand side of the equation is equal to the right-hand side, we can conclude that our solution is correct.

Conclusion

Solving linear equations is a straightforward process that involves isolating the variable and checking the solution. By following the steps outlined in this article, readers should be able to solve simple linear equations like $15.75 - x = -10.55$. Remember to always check your solution by plugging it back into the original equation.

Common Mistakes to Avoid

When solving linear equations, there are several common mistakes to avoid. These include:

• Not isolating the variable: Make sure to isolate the variable by adding or subtracting the same value from both sides of the equation.
• Not checking the solution: Always plug your solution back into the original equation to ensure that it is correct.
• Not following the order of operations: Make sure to follow the order of operations (PEMDAS) when simplifying expressions.

Real-World Applications

Linear equations have numerous real-world applications, including:

• Physics and engineering: Linear equations are used to describe the motion of objects and the behavior of electrical circuits.
• Economics: Linear equations are used to model the behavior of economic systems and to make predictions about future trends.
• Computer science: Linear equations are used in computer graphics and game development to create realistic simulations.

Final Thoughts

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Introduction

In our previous article, we covered the basics of solving linear equations. However, we know that practice makes perfect, and there's no better way to learn than by asking questions and getting answers. In this article, we'll provide a Q&A guide to help you better understand how 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 (in this case, $x$) is 1. Linear equations can be written in the form $ax + b = c$, where $a$, $b$, and $c$ are constants.

Q: How do I solve a linear equation?

A: To solve a linear equation, you need to isolate the variable. This can be done by adding or subtracting the same value from both sides of the equation. For example, if you have the equation $2x + 3 = 5$, you can subtract 3 from both sides to get $2x = 2$.

Q: What is the order of operations?

A: The order of operations is a set of rules that tells you which operations to perform first when simplifying expressions. The order of operations is:

1. Parentheses: Evaluate expressions inside parentheses first.
2. Exponents: Evaluate any exponential expressions next.
3. Multiplication and Division: Evaluate any multiplication and division operations from left to right.
4. Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

Q: How do I check my solution?

A: To check your solution, plug it back into the original equation. If the left-hand side of the equation is equal to the right-hand side, then your solution is correct.

Q: What are some common mistakes to avoid?

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

• Not isolating the variable: Make sure to isolate the variable by adding or subtracting the same value from both sides of the equation.
• Not checking the solution: Always plug your solution back into the original equation to ensure that it is correct.
• Not following the order of operations: Make sure to follow the order of operations (PEMDAS) when simplifying expressions.

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

A: To solve a linear equation with fractions, you need to eliminate the fractions by multiplying both sides of the equation by the least common multiple (LCM) of the denominators. For example, if you have the equation $\frac{1}{2}x + 3 = 5$, you can multiply both sides by 2 to get $x + 6 = 10$.

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

A: To solve a linear equation with decimals, you can use the same steps as solving a linear equation with fractions. For example, if you have the equation $2.5x + 3 = 5$, you can subtract 3 from both sides to get $2.5x = 2$.

Q: Can I use a calculator to solve linear equations?

A: Yes, you can use a calculator to solve linear equations. However, it's always a good idea to check your solution by plugging it back into the original equation.

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

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

• Physics and engineering: Linear equations are used to describe the motion of objects and the behavior of electrical circuits.
• Economics: Linear equations are used to model the behavior of economic systems and to make predictions about future trends.
• Computer science: Linear equations are used in computer graphics and game development to create realistic simulations.

Conclusion

Solving linear equations is a fundamental skill that is essential for success in mathematics and other fields. By following the steps outlined in this article and practicing with different types of equations, you'll become proficient in solving linear equations and apply them to real-world problems. Remember to always check your solution and to avoid common mistakes. With practice and patience, you'll become a master of solving linear equations!