Question

Write the interval (5,100] as an inequality and using set notation

Answer 1

The interval (5, 100] as an inequality is 5 < x ≤ 100.

The interval (5, 100] using set notation is x.

In Mathematics and Geometry, a domain is the set of all real numbers (x-values) for which a particular relation or function is defined.

The horizontal section of any graph is typically used for the representation of all domain values. Additionally, all domain values are both read and written by starting from smaller numerical values to larger numerical values, which means from the left of a graph to the right of the coordinate axis.

Note: The number part 5 is not part of the domain or solution because open parenthesis.

By critically observing the given domain written by using interval notation (5, 100], we can logically deduce the following domain written as inequality and using set notation:

The interval (5, 100] as an inequality is 5 < x ≤ 100.

The interval (5, 100] using set notation is 5 < x ≤ 100.

Answer 2

The inequality notation with bracket

[ ] when we want to include the end value
( ) when we don't want to include the end value

Interval (5, 100] means that 5 and 100 are the end values, we don't want to include the '5' but we want to include '100'

The inequality signs for not including end value is < and >
The inequality signs for including end value ≤ and ≥

(5, 100] = 5 < x ≤ 100