What does the addition property of equality state?

What does the addition property of equality state?

• A. Subtracting a number from both sides keeps the equation balanced
• B. Multiplying both sides by the same number maintains equality
• C. Adding the same number to both sides maintains equality
• D. Changing one side results in equal output on both sides

Answer: (C)

The addition property of equality states that if you add the same number to both sides of an equation, the two sides remain equal. This principle is fundamental in solving equations, as it allows for balanced manipulation of the equation without altering its truth. For example, if you have the equation \( x = 5 \) and you add 3 to both sides, you maintain equality, resulting in \( x + 3 = 8 \). This property underpins many arithmetic operations and algebraic techniques, making it essential for students to grasp as they progress in mathematics. Understanding this concept helps in solving equations efficiently and builds a foundation for more complex topics involving equality and manipulation of expressions.

The addition property of equality states that if you add the same number to both sides of an equation, the two sides remain equal. This principle is fundamental in solving equations, as it allows for balanced manipulation of the equation without altering its truth. For example, if you have the equation ( x = 5 ) and you add 3 to both sides, you maintain equality, resulting in ( x + 3 = 8 ).

This property underpins many arithmetic operations and algebraic techniques, making it essential for students to grasp as they progress in mathematics. Understanding this concept helps in solving equations efficiently and builds a foundation for more complex topics involving equality and manipulation of expressions.