Question

Which of the following illustrates the Addition Property of Inequalities?

If a b, then a + c > b + c
Both of these.
Neither of these.

Answer 1

The Addition Property of Inequalities states that adding the same number to both sides of an inequality retains its truth. This principle applies to any real numbers and is a fundamental concept in understanding inequalities.

Step-by-step explanation:

The Addition Property of Inequalities states that if you have two inequalities, such as a > b, and you add the same number c to both sides, the inequality remains true. In other words, a + c > b + c. This property allows you to maintain the relationship between the two sides of the inequality while changing their values.

For example, if we know that 2 > 1, and we add 3 to both sides, we get 5 > 4, which is still true. This demonstrates the concept that adding the same value to both sides of an inequality does not change its direction. It's important to realize that this property is valid for any real numbers, including fractions and decimals.

Answer 2

if a > b then a+c > b+c

adding the same number to two numbers doesn't change which one is bigger

If a is 10 and b is 6

it doesn't matter what c is. whatever you add to 10, the sum will always be more than adding it to 6

(obviously works with more than just 10 and 6 lol that was just an example)