Question

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

Answer 1

Inequality notation:
`y\leq 20`

Interval notation: ( - ∞, 20]

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

Answer 2

Inequality Notation:
`y\leq 20`

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

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`