Problem 69 - Introductory and Intermediate Algebra for College Students 4th

Question

State the addition property of equality and give an example.

Step-by-Step Solution

Answer

The Addition Property of Equality states that when the same number is added to both sides of an equation, the two sides remain equal. For instance, following this rule, if \(x = 2\), then by adding 3 to both sides the equation would become \(x + 3 = 2 + 3\), which simplifies to \(x + 3 = 5\).

Step 1: Definition of Addition Property of Equality

According to the Addition Property of Equality, if you add the same number to both sides of an equation, the two sides remain equal. Mathematically, this could be expressed as: for all real numbers \(a\), \(b\), and \(c\), if \(a = b\), then \(a + c = b + c\).

Step 2: Application Example

To illustrate this, let's take a simple equation: \(x = 5\). Applying the Addition Property of Equality by adding 3 to both sides we get: \(x + 3 = 5 + 3\). This simplifies down to \(x + 3 = 8\). This example illustrates that by adding the same value to both sides of the equation, the equation continues to hold.