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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 $w + 1.7 = 18.24$, where we need to isolate the variable $w$. We will break down the solution into step-by-step instructions, making it easy to understand and follow.

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 Solve

The equation we need to solve is $w + 1.7 = 18.24$. Our goal is to isolate the variable $w$ and find its value.

Step 1: Subtract 1.7 from Both Sides

To isolate $w$, we need to get rid of the constant term $1.7$ that is being added to it. We can do this by subtracting $1.7$ from both sides of the equation.

$$w + 1.7 - 1.7 = 18.24 - 1.7$$

This simplifies to:

$$w = 16.54$$

Step 2: Check the Solution

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

$$w + 1.7 = 18.24$$

Substituting $w = 16.54$, we get:

$$16.54 + 1.7 = 18.24$$

This is indeed true, so our solution is correct.

Conclusion

Solving linear equations is an essential skill in mathematics, and it requires a step-by-step approach. By following the instructions outlined in this article, we were able to solve the equation $w + 1.7 = 18.24$ and find the value of $w$. We hope that this article has provided a clear and concise guide to solving linear equations, and we encourage readers to practice solving equations on their own.

Tips and Tricks

Here are some tips and tricks to help you solve linear equations:

• Always read the equation carefully and identify the variable(s) and constants.
• Use inverse operations to isolate the variable(s).
• Check your solution by plugging it back into the original equation.
• Practice solving equations regularly to build your skills and confidence.

Common Mistakes to Avoid

Here are some common mistakes to avoid when solving linear equations:

• Not reading the equation carefully and making mistakes in the solution.
• Not using inverse operations to isolate the variable(s).
• Not checking the solution by plugging it back into the original equation.
• Not practicing solving equations regularly.

Real-World Applications

Linear equations have numerous real-world applications, including:

• Physics: Linear equations are used to describe the motion of objects, including velocity, acceleration, and distance.
• Engineering: Linear equations are used to design and optimize systems, including electrical circuits, mechanical systems, and computer networks.
• Economics: Linear equations are used to model economic systems, including supply and demand, inflation, and unemployment.
• Computer Science: Linear equations are used in algorithms and data structures, including sorting, searching, and graph theory.

Conclusion

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Introduction

In our previous article, we discussed how to solve linear equations of the form $w + 1.7 = 18.24$. We provided a step-by-step guide on how to isolate the variable $w$ and find its value. In this article, we will answer some frequently asked questions (FAQs) 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(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 solve a linear equation?

A: To solve a linear equation, you need to isolate the variable(s) by using inverse operations. For example, if you have an equation of the form $w + 1.7 = 18.24$, you can subtract 1.7 from both sides to isolate $w$.

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 making mistakes in the solution.
• Not using inverse operations to isolate the variable(s).
• Not checking the solution by plugging it back into the original equation.
• Not practicing solving equations regularly.

Q: How do I check my solution?

A: To check your solution, you need to plug it back into the original equation and verify that it satisfies the equation. For example, if you have an equation of the form $w + 1.7 = 18.24$ and you find that $w = 16.54$, you can plug this value back into the equation to verify that it is true.

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, including velocity, acceleration, and distance.
• Engineering: Linear equations are used to design and optimize systems, including electrical circuits, mechanical systems, and computer networks.
• Economics: Linear equations are used to model economic systems, including supply and demand, inflation, and unemployment.
• Computer Science: Linear equations are used in algorithms and data structures, including sorting, searching, and graph theory.

Q: How can I practice solving linear equations?

A: There are many ways to practice solving linear equations, including:

• Using online resources, such as Khan Academy or Mathway.
• Working with a tutor or teacher.
• Practicing with worksheets or exercises.
• Solving real-world problems that involve linear equations.

Q: What are some tips for solving linear equations?

A: Some tips for solving linear equations include:

• Always read the equation carefully and identify the variable(s) and constants.
• Use inverse operations to isolate the variable(s).
• Check your solution by plugging it back into the original equation.
• Practice solving equations regularly to build your skills and confidence.

Conclusion

Solving linear equations is a fundamental skill in mathematics, and it has numerous real-world applications. By following the instructions outlined in this article, we hope that you have a better understanding of how to solve linear equations and how to avoid common mistakes. We encourage you to practice solving equations regularly to build your skills and confidence.