To express the situation with all real numbers that are at most 95 or at least 55, we can break down the statement into two parts:
- The phrase “at most 95” means that the numbers can be equal to or less than 95. In inequality form, this can be written as: x ≤ 95.
- The phrase “at least 55” means that the numbers can be equal to or greater than 55. In inequality form, this can be expressed as: x ≥ 55.
Since these two conditions are combined using the word “or,” we can write the overall inequality as:
x ≤ 95 or x ≥ 55
This inequality encompasses all real numbers that either do not exceed 95 or are not less than 55. It’s important to note that this could also be represented using interval notation, where the solution is all real numbers that fall outside the open interval (55, 95), which can be denoted as:
(-
∞, 95] ∪ [55, +∞)
This notation reinforces the idea that we cover values lesser than or equal to 95 and greater than or equal to 55.