To Solve The Equation $3.7x - 15.9 = 2.97$, Use The Properties Of Equality. What Is The First Step To Solving The Equation?A. Subtract 15.9 From Both Sides Because It Is The Inverse Operation Of Addition.B. Add 15.9 To Both Sides Because It
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, $3.7x - 15.9 = 2.97$, using the properties of equality. We will break down the solution into manageable steps, making it easier for readers to understand and follow along.
Understanding the Properties of Equality
Before we dive into solving the equation, it's essential to understand the properties of equality. The properties of equality state that if two expressions are equal, then we can perform the same operation on both sides of the equation without changing the equality. There are three main properties of equality:
- Addition Property of Equality: If $a = b$, then $a + c = b + c$.
- Subtraction Property of Equality: If $a = b$, then $a - c = b - c$.
- Multiplication Property of Equality: If $a = b$, then $ac = bc$.
- Division Property of Equality: If $a = b$ and $c \neq 0$, then $\frac{a}{c} = \frac{b}{c}$.
The First Step to Solving the Equation
Now that we have a solid understanding of the properties of equality, let's apply them to the given equation, $3.7x - 15.9 = 2.97$. The first step to solving the equation is to isolate the variable $x$. To do this, we need to get rid of the constant term, $-15.9$, that is being subtracted from $3.7x$. Since subtraction is the inverse operation of addition, we can add $15.9$ to both sides of the equation to eliminate the constant term.
Why Add 15.9 to Both Sides?
Adding $15.9$ to both sides of the equation is the correct step because it is the inverse operation of subtraction. When we subtract $15.9$ from $3.7x$, we are essentially removing the constant term from the left side of the equation. By adding $15.9$ to both sides, we are "reversing" the subtraction operation and isolating the variable $x$.
The Correct Answer
The correct answer is B. Add 15.9 to both sides because it is the inverse operation of subtraction.
Conclusion
Solving linear equations requires a clear understanding of the properties of equality. By applying these properties, we can isolate the variable and solve for its value. In this article, we have demonstrated the first step to solving the equation $3.7x - 15.9 = 2.97$, which is to add $15.9$ to both sides of the equation. This step is essential in isolating the variable $x$ and solving for its value.
Additional Tips and Tricks
Here are some additional tips and tricks to help you solve linear equations:
- Use the correct inverse operation: When solving an equation, make sure to use the correct inverse operation. For example, if you have an equation with addition, use subtraction to isolate the variable.
- Check your work: Always check your work by plugging the solution back into the original equation. This will help you ensure that your solution is correct.
- Use algebraic properties: Algebraic properties, such as the commutative and associative properties, can help you simplify equations and solve for the variable.
By following these tips and tricks, you can become proficient in solving linear equations and tackle even the most challenging problems with confidence.
Common Mistakes to Avoid
Here are some common mistakes to avoid when solving linear equations:
- Not using the correct inverse operation: Failing to use the correct inverse operation can lead to incorrect solutions.
- Not checking your work: Not checking your work can result in incorrect solutions.
- Not using algebraic properties: Failing to use algebraic properties can make it difficult to simplify equations and solve for the variable.
By avoiding these common mistakes, you can ensure that your solutions are accurate and reliable.
Real-World Applications
Linear equations have numerous real-world applications, including:
- Physics and engineering: Linear equations are used to model real-world phenomena, such as motion and energy.
- Economics: Linear equations are used to model economic systems and make predictions about economic trends.
- Computer science: Linear equations are used in computer science to solve problems and make predictions.
By understanding how to solve linear equations, you can apply this knowledge to a wide range of real-world problems and make a meaningful impact in your field.
Conclusion
Introduction
In our previous article, we explored the first step to solving the equation $3.7x - 15.9 = 2.97$, which is to add $15.9$ to both sides of the equation. In this article, we will continue to provide a comprehensive guide to solving linear equations, this time in the form of a Q&A.
Q: What is the purpose of solving linear equations?
A: Solving linear equations is a fundamental skill that has numerous real-world applications. It allows us to model and solve problems in various fields, such as physics, engineering, economics, and computer science.
Q: What are the properties of equality?
A: The properties of equality state that if two expressions are equal, then we can perform the same operation on both sides of the equation without changing the equality. There are four main properties of equality:
- Addition Property of Equality: If $a = b$, then $a + c = b + c$.
- Subtraction Property of Equality: If $a = b$, then $a - c = b - c$.
- Multiplication Property of Equality: If $a = b$, then $ac = bc$.
- Division Property of Equality: If $a = b$ and $c \neq 0$, then $\frac{a}{c} = \frac{b}{c}$.
Q: How do I isolate the variable in a linear equation?
A: To isolate the variable in a linear equation, you need to get rid of the constant term that is being added or subtracted from the variable. This can be done by using the inverse operation of addition or subtraction.
Q: What is the inverse operation of addition?
A: The inverse operation of addition is subtraction. When you subtract a number from another number, you are essentially removing the constant term from the left side of the equation.
Q: What is the inverse operation of subtraction?
A: The inverse operation of subtraction is addition. When you add a number to another number, you are essentially "reversing" the subtraction operation and isolating the variable.
Q: How do I check my work when solving a linear equation?
A: To check your work, plug the solution back into the original equation. If the solution is correct, the equation should be true. If the solution is incorrect, the equation will be false.
Q: What are some common mistakes to avoid when solving linear equations?
A: Some common mistakes to avoid when solving linear equations include:
- Not using the correct inverse operation: Failing to use the correct inverse operation can lead to incorrect solutions.
- Not checking your work: Not checking your work can result in incorrect solutions.
- Not using algebraic properties: Failing to use algebraic properties can make it difficult to simplify equations and solve for the variable.
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 model real-world phenomena, such as motion and energy.
- Economics: Linear equations are used to model economic systems and make predictions about economic trends.
- Computer science: Linear equations are used in computer science to solve problems and make predictions.
Conclusion
Solving linear equations is a fundamental skill that requires a clear understanding of the properties of equality. By applying these properties, we can isolate the variable and solve for its value. In this article, we have provided a comprehensive Q&A guide to solving linear equations, covering topics such as the purpose of solving linear equations, the properties of equality, and common mistakes to avoid. By following these steps and avoiding common mistakes, you can become proficient in solving linear equations and tackle even the most challenging problems with confidence.