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Chapter 2: Problem 69

State the addition property of equality and give an example.

Short Answer

Expert verified
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 by step solution

01

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 \(a + c = b + c\).
02

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.

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Most popular questions from this chapter

Solve each inequality. Use a calculator to help with the arithmetic. $$1.45-7.23 x>-1.442$$

Use both the addition and multiplication properties of inequality to solve each inequality and graph the solution set on a number line. $$7-2(x-4)<5(1-2 x)$$

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