Using interval notal to represent inequalities, the following are put into consideration:
1. With inequalities, we use "less than": < or "greater than": > to exclude the endpoint of the interval. With interval notation, we use round parentheses, ( or ).
2. With inequalities, we use "less than or equal to": ≤ or "greater than or equal to": ≥ to include the endpoint of the interval. With interval notation, we use square brackets, [ or ].
3. To combine two intervals, use U (an uppercase letter u) for union: ∪; Use oo (two lowercase letter o's) for infinity: ∞
Given the inequality below
[tex]5\leq x>7[/tex]
It can be observed that 5 is less than or equal to x, which means 5 is inclusive, we would then use a square bracket, [ , for 5.
It can also be observed that x is greater than 7, which means 7 is exclusive, we would then use round parenthesis, ).
Hence, the interval notation is [5,7), OPTION C
The representation of the inequality using number line is as shown below:
Hence, the correct number line from the options is OPTION B
