Question

Use inequality notation and interval notation to describe y is no more than 20

Answer 1

Answer:

Inequality Notation:  $y\leq 20$

Interval Notation: $(-\infty , 20]$

Step-by-step explanation:

Inequality Notation: It is like an equation that uses symbols for :

*Less than  - '<'

* Less than or equal to -  '$\leq$'

*Greater than -  ' >'

* Greater than or equal to - $'\geq '$

and Equal to -  '='

Interval Notation: In this we just write the beginning and ending numbers of the interval, and we use:

* [ ] - Square bracket when we want to include the end value, or

* ( ) - Round bracket when we don't include the value.

To describe y is no more than 20.

As no more than means no greater than or not above.

then, y is no more than 20 which implies $y\leq 20$

Therefore, the Interval notation for y is no more than 20 is ; $(-\infty , 20]$ and the inequality notation is; $y\leq 20$

Answer 2

Answer:

Inequality notation: $y\leq 20$

Interval notation: ( - ∞, 20]

Step-by-step explanation:

"y is no more than 20"

means y is NOT larger than 20, but less than AND also equal to 20.

This can be written with inequality sign as $y\leq20$

In interval notation,

• We use "(" or ")" sign to mean inequality ONLY ( "<" or ">" )
• When we want to include EQUALS TO with "<" or ">", then we use "[" or "]" sign.

So $y\leq20$ would mean that y is from -∞ till 20, where 20 is INCLUDED.

Hence, we can write (-∞,20] in interval notation.

Note:

The "(" before -∞ indicates that it is not included (infinity is not a number, but a concept so you can't equate something to infinity)

The "]" after 20 indicates that 20 is INCLUDED in the inequality