What Property Was Applied To Solve The Equation Below?$\[ \begin{aligned} -\frac{3}{8} X & = 48 \\ -\frac{3}{8}\left(-\frac{8}{3}\right) X & = 48\left(-\frac{8}{3}\right) \\ x & = -128 \end{aligned} \\]A. Addition Property Of Equality B.

by ADMIN 239 views

Introduction

In mathematics, solving equations is a fundamental concept that involves manipulating expressions to isolate the variable. When solving equations, we often apply various properties to simplify the equation and find the value of the variable. In this article, we will explore the property that was applied to solve the given equation.

The Given Equation

The given equation is:

−38x=48-\frac{3}{8} x = 48

To solve this equation, we need to isolate the variable x. We can start by multiplying both sides of the equation by the reciprocal of the coefficient of x, which is -8/3.

Applying the Property

When we multiply both sides of the equation by -8/3, we are applying the Multiplication Property of Equality. This property states that if we multiply or divide both sides of an equation by the same non-zero value, the equation remains true.

In this case, we are multiplying both sides of the equation by -8/3, which is the reciprocal of the coefficient of x. This allows us to eliminate the coefficient and isolate the variable x.

The Solution

After applying the Multiplication Property of Equality, we get:

−38(−83)x=48(−83)-\frac{3}{8}\left(-\frac{8}{3}\right) x = 48\left(-\frac{8}{3}\right)

Simplifying the equation, we get:

x=−128x = -128

Conclusion

In conclusion, the property that was applied to solve the given equation is the Multiplication Property of Equality. This property allows us to multiply or divide both sides of an equation by the same non-zero value, which helps us to isolate the variable and solve the equation.

The Importance of Properties in Mathematics

Properties play a crucial role in mathematics, as they provide a set of rules that help us to manipulate equations and solve problems. By understanding and applying these properties, we can simplify complex equations and find the value of the variable.

Types of Properties in Mathematics

There are several types of properties in mathematics, including:

  • Addition Property of Equality: This property states that if we add the same value to both sides of an equation, the equation remains true.
  • Subtraction Property of Equality: This property states that if we subtract the same value from both sides of an equation, the equation remains true.
  • Multiplication Property of Equality: This property states that if we multiply or divide both sides of an equation by the same non-zero value, the equation remains true.
  • Division Property of Equality: This property states that if we divide both sides of an equation by the same non-zero value, the equation remains true.

Real-World Applications of Properties

Properties have numerous real-world applications, including:

  • Algebra: Properties are used to solve equations and manipulate expressions in algebra.
  • Geometry: Properties are used to prove theorems and solve problems in geometry.
  • Trigonometry: Properties are used to solve equations and manipulate expressions in trigonometry.
  • Calculus: Properties are used to solve equations and manipulate expressions in calculus.

Final Thoughts

In conclusion, the property that was applied to solve the given equation is the Multiplication Property of Equality. This property is a fundamental concept in mathematics that helps us to manipulate equations and solve problems. By understanding and applying properties, we can simplify complex equations and find the value of the variable.

References

  • [1] "Algebra" by Michael Artin
  • [2] "Geometry" by Michael Spivak
  • [3] "Trigonometry" by Charles P. McKeague
  • [4] "Calculus" by Michael Spivak

Further Reading

  • [1] "Properties of Equality" by Math Open Reference
  • [2] "Multiplication Property of Equality" by Mathway
  • [3] "Division Property of Equality" by Khan Academy

Related Articles

  • [1] "Solving Equations with Variables on Both Sides"
  • [2] "Simplifying Expressions with Variables"
  • [3] "Proving Theorems in Geometry"

Tags

  • Multiplication Property of Equality
  • Division Property of Equality
  • Addition Property of Equality
  • Subtraction Property of Equality
  • Properties of Equality
  • Solving Equations
  • Manipulating Expressions
  • Algebra
  • Geometry
  • Trigonometry
  • Calculus

Introduction

In our previous article, we discussed the property that was applied to solve the given equation. In this article, we will answer some frequently asked questions about properties of equality in mathematics.

Q: What is the Multiplication Property of Equality?

A: The Multiplication Property of Equality states that if we multiply or divide both sides of an equation by the same non-zero value, the equation remains true. This property is used to eliminate coefficients and isolate the variable.

Q: What is the Division Property of Equality?

A: The Division Property of Equality states that if we divide both sides of an equation by the same non-zero value, the equation remains true. This property is used to eliminate coefficients and isolate the variable.

Q: What is the Addition Property of Equality?

A: The Addition Property of Equality states that if we add the same value to both sides of an equation, the equation remains true. This property is used to eliminate constants and isolate the variable.

Q: What is the Subtraction Property of Equality?

A: The Subtraction Property of Equality states that if we subtract the same value from both sides of an equation, the equation remains true. This property is used to eliminate constants and isolate the variable.

Q: How do I apply the properties of equality to solve equations?

A: To apply the properties of equality, follow these steps:

  1. Identify the equation and the variable you want to isolate.
  2. Determine which property to apply (addition, subtraction, multiplication, or division).
  3. Apply the property to both sides of the equation.
  4. Simplify the equation and isolate the variable.

Q: What are some common mistakes to avoid when applying properties of equality?

A: Some common mistakes to avoid when applying properties of equality include:

  • Not checking if the value is zero before dividing.
  • Not simplifying the equation after applying the property.
  • Not isolating the variable after applying the property.

Q: How do I know which property to apply to a given equation?

A: To determine which property to apply, follow these steps:

  1. Look at the equation and identify the variable you want to isolate.
  2. Determine if the equation has a coefficient or a constant.
  3. Choose the property that will eliminate the coefficient or constant and isolate the variable.

Q: Can I apply multiple properties to a single equation?

A: Yes, you can apply multiple properties to a single equation. However, be careful to apply the properties in the correct order and to simplify the equation after each application.

Q: What are some real-world applications of properties of equality?

A: Properties of equality have numerous real-world applications, including:

  • Algebra: Properties are used to solve equations and manipulate expressions in algebra.
  • Geometry: Properties are used to prove theorems and solve problems in geometry.
  • Trigonometry: Properties are used to solve equations and manipulate expressions in trigonometry.
  • Calculus: Properties are used to solve equations and manipulate expressions in calculus.

Q: Can I use properties of equality to solve inequalities?

A: Yes, you can use properties of equality to solve inequalities. However, be careful to apply the properties in the correct order and to simplify the inequality after each application.

Q: What are some common types of equations that require the use of properties of equality?

A: Some common types of equations that require the use of properties of equality include:

  • Linear equations
  • Quadratic equations
  • Polynomial equations
  • Rational equations

Q: How do I know if I have applied the properties of equality correctly?

A: To determine if you have applied the properties of equality correctly, follow these steps:

  1. Check if the equation is true after applying the property.
  2. Simplify the equation and isolate the variable.
  3. Verify that the solution is correct.

References

  • [1] "Algebra" by Michael Artin
  • [2] "Geometry" by Michael Spivak
  • [3] "Trigonometry" by Charles P. McKeague
  • [4] "Calculus" by Michael Spivak

Further Reading

  • [1] "Properties of Equality" by Math Open Reference
  • [2] "Multiplication Property of Equality" by Mathway
  • [3] "Division Property of Equality" by Khan Academy

Related Articles

  • [1] "Solving Equations with Variables on Both Sides"
  • [2] "Simplifying Expressions with Variables"
  • [3] "Proving Theorems in Geometry"

Tags

  • Multiplication Property of Equality
  • Division Property of Equality
  • Addition Property of Equality
  • Subtraction Property of Equality
  • Properties of Equality
  • Solving Equations
  • Manipulating Expressions
  • Algebra
  • Geometry
  • Trigonometry
  • Calculus