Rahul Solved The Equation 2 ( X − 1 8 ) − 3 5 X = 55 4 2\left(x-\frac{1}{8}\right)-\frac{3}{5} X=\frac{55}{4} 2 ( X − 8 1 ) − 5 3 X = 4 55 . In Which Step Did He Use The Addition Property Of Equality?Rahul's Solution:$[ \begin{array}{|c|c|} \hline \text{Steps} & \text{Resulting Equations}

Mar 9, 2025 by ADMIN 296 views

Rahul's Equation Solution: Identifying the Addition Property of Equality

In mathematics, the addition property of equality is a fundamental concept that allows us to add or subtract the same value to both sides of an equation without changing the solution. This property is essential in solving linear equations and is a crucial step in many mathematical problems. In this article, we will analyze Rahul's solution to the equation $2\left(x-\frac{1}{8}\right)-\frac{3}{5} x=\frac{55}{4}$ and identify the step where he used the addition property of equality.

Rahul's solution to the equation is as follows:

{ \begin{array}{|c|c|} \hline \text{Steps} & \text{Resulting equations} \\\hline 1 & 2\left(x-\frac{1}{8}\right)-\frac{3}{5} x=\frac{55}{4} \\ 2 & 2x-\frac{1}{4}-\frac{3}{5} x=\frac{55}{4} \\ 3 & 2x-\frac{3}{5} x=\frac{55}{4}+\frac{1}{4} \\ 4 & \frac{10}{5}x-\frac{3}{5} x=\frac{56}{4} \\ 5 & \frac{7}{5} x=\frac{56}{4} \\ 6 & x=\frac{56}{4} \cdot \frac{5}{7} \\ 7 & x=\frac{140}{28} \\ 8 & x=5 \end{array} }

Identifying the Addition Property of Equality

To identify the step where Rahul used the addition property of equality, we need to examine each step of his solution. The addition property of equality states that if we add or subtract the same value to both sides of an equation, the solution remains the same.

In step 3 of Rahul's solution, he added $\frac{1}{4}$ to both sides of the equation:

$2x-\frac{3}{5} x=\frac{55}{4}+\frac{1}{4}$

This is an example of the addition property of equality, where Rahul added the same value ( $\frac{1}{4}$ ) to both sides of the equation.

In conclusion, Rahul used the addition property of equality in step 3 of his solution to the equation $2\left(x-\frac{1}{8}\right)-\frac{3}{5} x=\frac{55}{4}$ . This step is essential in solving linear equations and is a fundamental concept in mathematics.

Importance of the Addition Property of Equality

The addition property of equality is a crucial concept in mathematics that allows us to simplify equations and solve for the unknown variable. It is essential to understand this property and apply it correctly in order to solve linear equations and other mathematical problems.

Real-World Applications

The addition property of equality has many real-world applications in fields such as physics, engineering, and economics. For example, in physics, the addition property of equality is used to solve problems involving motion and forces. In engineering, it is used to design and optimize systems. In economics, it is used to analyze and solve problems involving financial markets and trade.

Tips for Solving Linear Equations

When solving linear equations, it is essential to apply the addition property of equality correctly. Here are some tips to help you solve linear equations:

Start by simplifying the equation by combining like terms.
Use the addition property of equality to add or subtract the same value to both sides of the equation.
Use the multiplication property of equality to multiply or divide both sides of the equation by the same value.
Check your solution by plugging it back into the original equation.

By following these tips and understanding the addition property of equality, you can solve linear equations and other mathematical problems with confidence.

Common Mistakes to Avoid

When solving linear equations, there are several common mistakes to avoid. Here are some of the most common mistakes:

Failing to simplify the equation by combining like terms.
Failing to apply the addition property of equality correctly.
Failing to check the solution by plugging it back into the original equation.
Making errors when multiplying or dividing both sides of the equation by the same value.

By avoiding these common mistakes and understanding the addition property of equality, you can solve linear equations and other mathematical problems with confidence.

In conclusion, the addition property of equality is a fundamental concept in mathematics that allows us to add or subtract the same value to both sides of an equation without changing the solution. Rahul used this property in step 3 of his solution to the equation $2\left(x-\frac{1}{8}\right)-\frac{3}{5} x=\frac{55}{4}$ . By understanding and applying this property correctly, you can solve linear equations and other mathematical problems with confidence.
Frequently Asked Questions: Addition Property of Equality

The addition property of equality is a fundamental concept in mathematics that allows us to add or subtract the same value to both sides of an equation without changing the solution. In this article, we will answer some frequently asked questions about the addition property of equality.

Q: What is the addition property of equality?

A: The addition property of equality states that if we add or subtract the same value to both sides of an equation, the solution remains the same.

Q: Why is the addition property of equality important?

A: The addition property of equality is essential in solving linear equations and is a crucial concept in mathematics. It allows us to simplify equations and solve for the unknown variable.

Q: How do I apply the addition property of equality?

A: To apply the addition property of equality, you need to add or subtract the same value to both sides of the equation. For example, if you have the equation $x + 3 = 7$ , you can add 3 to both sides to get $x = 10$ .

Q: What are some common mistakes to avoid when applying the addition property of equality?

A: Some common mistakes to avoid when applying the addition property of equality include:

Failing to simplify the equation by combining like terms.
Failing to apply the addition property of equality correctly.
Failing to check the solution by plugging it back into the original equation.
Making errors when multiplying or dividing both sides of the equation by the same value.

Q: How do I check my solution to an equation?

A: To check your solution to an equation, you need to plug it back into the original equation and verify that it is true. For example, if you have the equation $x + 3 = 7$ and you solve for $x$ to get $x = 10$ , you can plug $x = 10$ back into the original equation to get $10 + 3 = 7$ , which is true.

Q: What are some real-world applications of the addition property of equality?

A: The addition property of equality has many real-world applications in fields such as physics, engineering, and economics. For example, in physics, the addition property of equality is used to solve problems involving motion and forces. In engineering, it is used to design and optimize systems. In economics, it is used to analyze and solve problems involving financial markets and trade.

Q: How do I use the addition property of equality to solve linear equations?

A: To use the addition property of equality to solve linear equations, you need to follow these steps:

Simplify the equation by combining like terms.
Add or subtract the same value to both sides of the equation.
Check your solution by plugging it back into the original equation.

Q: What are some tips for solving linear equations?

A: Some tips for solving linear equations include:

Start by simplifying the equation by combining like terms.
Use the addition property of equality to add or subtract the same value to both sides of the equation.
Use the multiplication property of equality to multiply or divide both sides of the equation by the same value.
Check your solution by plugging it back into the original equation.

In conclusion, the addition property of equality is a fundamental concept in mathematics that allows us to add or subtract the same value to both sides of an equation without changing the solution. By understanding and applying this property correctly, you can solve linear equations and other mathematical problems with confidence.