Question

Which property of inequalities states that if x ≤ 5 and 5 ≤ y , then x ≤ y?

Answer 1

Hello!

The answer is: The transitive property.

Why?

Inequalities express the relative size between two values/numbers.

The transitive property of inequalities states that there's a way to relate two or more inequalities when they have at least a common value, and we can use it to create a relationship with a third or more values/variables.

For your statement, we have

A common value which is 5

Two inequalities expressing a relative size between two variables and a common value which is 5:

`x\leq 5\\5\leq y`

So, the inequalities are telling us that the common value (5) is higher or equal than x

and, the variable y is higher or equal than 5

So, using the transitive property we can safely assume that, y is higher or equal, than x

`x\leq y`

Have a nice day!

Answer 2

Transitive property of inequality.

Explanation:

Transitive property of inequality states that if

`a\leq b\text{ and }b\leq c\text{ then }a\leq c`

`a\geq b\text{ and }b\geq c\text{ then }a\geq c`

Now, the given conditions are x ≤ 5 and 5 ≤ y, then x ≤ y

It is same as the transitive property stated above. When we compare, we get

a = x, b = 5, c = y

Therefore, the given inequalities is transitive property of inequality.