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📘intermediate algebra review

key term - Identity Property of Equality

Citation:

Definition

The identity property of equality states that any expression or equation is equal to itself. This means that for any value of a variable, if both sides of an equation are the same, the equation will always be true.

5 Must Know Facts For Your Next Test

  1. The identity property of equality is fundamental to solving linear equations using a general strategy.
  2. It allows you to isolate a variable by performing the same operations on both sides of an equation.
  3. Applying the identity property ensures that the original equation and the simplified equation are equivalent.
  4. Understanding the identity property is crucial for verifying the solution to a linear equation is correct.
  5. The identity property is often used in conjunction with other properties of equality to manipulate equations.

Review Questions

  • Explain how the identity property of equality is used when solving linear equations.
    • The identity property of equality states that an expression is equal to itself. This allows you to perform the same operations on both sides of a linear equation to isolate the variable. For example, if you have the equation $2x + 5 = 17$, you can subtract 5 from both sides to get $2x = 12$, and then divide both sides by 2 to find $x = 6$. The identity property ensures that each step maintains the equivalence of the original equation.
  • Describe how the identity property of equality is related to the other properties of equality, such as the reflexive, symmetric, and substitution properties.
    • The identity property of equality is closely linked to the other properties of equality. The reflexive property states that any expression is equal to itself, which is the foundation of the identity property. The symmetric property allows you to reverse the order of an equation, while the substitution property permits replacing an expression with an equivalent one. Together, these properties form the basis for manipulating equations and maintaining the equality between the two sides. The identity property is often used in conjunction with these other properties when solving linear equations using a general strategy.
  • Analyze how the understanding of the identity property of equality contributes to the verification of solutions to linear equations.
    • Verifying the solution to a linear equation is crucial, and the identity property of equality plays a key role in this process. By understanding that an expression is equal to itself, you can substitute the proposed solution back into the original equation and confirm that both sides are indeed equal. This ensures that the steps taken to solve the equation were correct and that the final solution satisfies the original equation. The identity property provides the framework for this verification process, allowing you to check the validity of the solution and have confidence in the accuracy of your work.