Addition property of equality

Oct 13, 2025 by talynt.org 112 views

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 linear equation using the distributive property, addition property of equality, and division property of equality. We will use a specific equation as an example to illustrate these steps.

The Equation

The equation we will be solving is:

2.6(5.5p - 12.4) = 127.92

Our goal is to isolate the variable $p$ and find its value.

Step 1: Distributive Property

The first step in solving this equation is to apply the distributive property. This property states that for any real numbers $a$ , $b$ , and $c$ , the following equation holds:

a(b + c) = ab + ac

In our equation, we have:

2.6(5.5p - 12.4) = 2.6(5.5p) - 2.6(12.4)

Using the distributive property, we can rewrite the equation as:

14.3p - 32.24 = 127.92

Step 2: Addition Property of Equality

The next step is to add $32.24$ to both sides of the equation to isolate the term with the variable $p$ . This is known as the addition property of equality, which states that for any real numbers $a$ and $b$ , the following equation holds:

a = b \Rightarrow a + c = b + c

Applying this property to our equation, we get:

14.3p - 32.24 + 32.24 = 127.92 + 32.24

Simplifying the equation, we get:

14.3p = 160.16

Step 3: Division Property of Equality

The final step is to divide both sides of the equation by $14.3$ to solve for $p$ . This is known as the division property of equality, which states that for any real numbers $a$ and $b$ , the following equation holds:

a = b \Rightarrow \frac{a}{c} = \frac{b}{c}

Applying this property to our equation, we get:

\frac{14.3p}{14.3} = \frac{160.16}{14.3}

Simplifying the equation, we get:

p = 11.21

Conclusion

In this article, we have solved a linear equation using the distributive property, addition property of equality, and division property of equality. We have shown that by applying these properties in a step-by-step manner, we can isolate the variable $p$ and find its value. This is a crucial skill for students and professionals alike, and we hope that this article has provided a clear and concise guide to solving linear equations.

Real-World Applications

Linear equations have numerous real-world applications in fields such as physics, engineering, economics, and computer science. For example, in physics, linear equations are used to describe the motion of objects under the influence of forces. In engineering, linear equations are used to design and optimize systems such as bridges, buildings, and electrical circuits. In economics, linear equations are used to model the behavior of markets and make predictions about future trends. In computer science, linear equations are used to solve problems in machine learning and data analysis.

Tips and Tricks

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

Always start by applying the distributive property to simplify the equation.
Use the addition property of equality to isolate the term with the variable.
Use the division property of equality to solve for the variable.
Check your work by plugging the solution back into the original equation.
Practice, practice, practice! Solving linear equations is a skill that takes time and practice to develop.

Common Mistakes

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

Failing to apply the distributive property.
Failing to use the addition property of equality.
Failing to use the division property of equality.
Not checking your work.
Not practicing regularly.

Conclusion

Introduction

In our previous article, we provided a step-by-step guide to solving linear equations using the distributive property, addition property of equality, and division property of equality. In this article, we will answer some of the most 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 is 1. In other words, it is an equation in which the variable is not raised to a power greater than 1.

Q: What are the properties of equality?

A: The properties of equality are:

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, then a/c = b/c.

Q: How do I solve a linear equation?

A: To solve a linear equation, follow these steps:

Apply the distributive property to simplify the equation.
Use the addition property of equality to isolate the term with the variable.
Use the division property of equality to solve for the variable.

Q: What is the distributive property?

A: The distributive property is a property of arithmetic that states that for any real numbers a, b, and c, the following equation holds:

a(b + c) = ab + ac

Q: How do I apply the distributive property?

A: To apply the distributive property, simply multiply the term outside the parentheses by each term inside the parentheses.

Q: What is the addition property of equality?

A: The addition property of equality states that if a = b, then a + c = b + c.

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

A: To use the addition property of equality, simply add the same value to both sides of the equation.

Q: What is the division property of equality?

A: The division property of equality states that if a = b, then a/c = b/c.

Q: How do I use the division property of equality?

A: To use the division property of equality, simply divide both sides of the equation by the same value.

Q: What are some common mistakes to avoid when solving linear equations?

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

Failing to apply the distributive property.
Failing to use the addition property of equality.
Failing to use the division property of equality.
Not checking your work.
Not practicing regularly.

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 problems.
Solving real-world problems that involve linear equations.

Conclusion

In conclusion, solving linear equations is a crucial skill for students and professionals alike. By understanding the properties of equality and following the steps outlined in this article, you can solve linear equations with confidence. Remember to practice regularly and avoid common mistakes to become proficient in solving linear equations.