Question

I need help with a Set-Builder and interval notation problem. I will include a picture. Thank you so much!

Answer 1

`\begin{gathered} Interval\text{ notation: }\lbrack-1,\text{ 1}\rbrack \\ \text{see number line below} \end{gathered}`Step-by-step explanation:
`\begin{gathered} The\text{ given set:} \\ -1\text{ }\le\text{ x }\le\text{ 1} \end{gathered}`

To plot the set above on the number line, we need to consider the inequality in the set at the start and end point.

The inequality is ≤. The equal to sign mena the circle will be shaded.

The line will between the -1 and 1 (this shows x is greater than -1 or equal to but less than or equal to 1)

plotting on a number line:

For the interval notation:

The inequality is ≤. When we have an equal sign attached to an inquality, it means the number close to it is included in the set. In our set, the ≤ is after -1 and before 1. This indicate -1 and 1 are included in the set.

In interval notation, For inequality with equal sign, the symbol [ ] are used to indicate the numbers are included. while the symbol ( ) are used to indicate the numbers are not included.

Representing our set -1 ≤ x ≤ 1 in interval notation:

`\lbrack-1,\text{ 1}\rbrack`