What is the addition property of inequalities?

The addition property of inequalities states that adding the same number to both sides of an inequality does not change the inequality's direction.

In other words:

• If a > b, then a + c > b + c for any real number c.
• If a < b, then a + c < b + c for any real number c.
• If a ≥ b, then a + c ≥ b + c for any real number c.
• If a ≤ b, then a + c ≤ b + c for any real number c.

This property holds true regardless of whether c is positive, negative, or zero. It is a fundamental principle used to solve inequalities algebraically.

Example:

Let's say we have the inequality: x - 3 < 5

To solve for x, we can add 3 to both sides of the inequality without changing the direction of the inequality:

x - 3 + 3 < 5 + 3

This simplifies to:

x < 8

Therefore, the addition property allows us to isolate the variable and solve the inequality.