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

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Introduction

When solving equations, it's essential to understand the properties of equality that allow us to manipulate the equations and find the solution. In this article, we'll explore the property that was applied to solve the given equation.

The Equation

The given equation is:

−38x=48-\frac{3}{8} x=48

Applying the Property

To solve this equation, we need to apply a specific property of equality. The property that was applied in this case is the Multiplication Property of Equality.

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.

In this case, we multiplied both sides of the equation by −83-\frac{8}{3}, which is the reciprocal of −38-\frac{3}{8}. This is a valid operation because the reciprocal of a fraction is the fraction with the numerator and denominator swapped.

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 left-hand side, 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 is essential for solving equations.

The Importance of Properties of Equality

Properties of equality are fundamental concepts in mathematics that allow us to manipulate equations and find solutions. Understanding these properties is crucial for solving equations, whether it's in algebra, geometry, or other areas of mathematics.

Common Properties of Equality

There are several properties of equality that are commonly used to solve equations. Some of these properties include:

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

Real-World Applications

Properties of equality have numerous real-world applications. For example, in physics, we use equations to describe the motion of objects. In economics, we use equations to model the behavior of markets. In computer science, we use equations to optimize algorithms.

Conclusion

In conclusion, the property that was applied to solve the given equation is the Multiplication Property of Equality. Understanding properties of equality is essential for solving equations and has numerous real-world applications.

Frequently Asked Questions

  • What is the Multiplication Property of Equality? 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.
  • What is the Addition Property of Equality? The Addition Property of Equality states that if we add the same value to both sides of an equation, the equation remains true.
  • What is the Subtraction Property of Equality? The Subtraction Property of Equality states that if we subtract the same value from both sides of an equation, the equation remains true.
  • What is the Division Property of Equality? 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.

References

  • [1] "Algebra" by Michael Artin
  • [2] "Calculus" by Michael Spivak
  • [3] "Linear Algebra" by Jim Hefferon

Further Reading

  • [1] "Properties of Equality" by Khan Academy
  • [2] "Solving Equations" by Mathway
  • [3] "Algebra" by MIT OpenCourseWare

Introduction

Properties of equality are fundamental concepts in mathematics that allow us to manipulate equations and find solutions. In this article, we'll answer some frequently asked questions about properties of equality.

Q&A

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.

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.

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.

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.

Q: Can I add or subtract the same value from both sides of an equation?

A: Yes, you can add or subtract the same value from both sides of an equation. This is known as the Addition Property of Equality and the Subtraction Property of Equality.

Q: Can I multiply or divide both sides of an equation by the same non-zero value?

A: Yes, you can multiply or divide both sides of an equation by the same non-zero value. This is known as the Multiplication Property of Equality and the Division Property of Equality.

Q: What happens if I multiply or divide both sides of an equation by zero?

A: If you multiply or divide both sides of an equation by zero, the equation becomes undefined. This is because division by zero is not allowed in mathematics.

Q: Can I use properties of equality to solve equations with variables on both sides?

A: Yes, you can use properties of equality to solve equations with variables on both sides. For example, if you have an equation like x + 2 = 5, you can subtract 2 from both sides to get x = 3.

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

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

  • Multiplying or dividing both sides of an equation by zero
  • Adding or subtracting different values from both sides of an equation
  • Not following the order of operations when simplifying expressions

Q: How do I know which property of equality to use when solving an equation?

A: To determine which property of equality to use when solving an equation, you need to look at the equation and determine what operation needs to be performed to isolate the variable. For example, if you have an equation like x + 2 = 5, you can subtract 2 from both sides to get x = 3.

Conclusion

In conclusion, properties of equality are fundamental concepts in mathematics that allow us to manipulate equations and find solutions. By understanding these properties, you can solve equations with confidence and accuracy.

Further Reading

  • [1] "Properties of Equality" by Khan Academy
  • [2] "Solving Equations" by Mathway
  • [3] "Algebra" by MIT OpenCourseWare

References

  • [1] "Algebra" by Michael Artin
  • [2] "Calculus" by Michael Spivak
  • [3] "Linear Algebra" by Jim Hefferon