How do you write an inequality for the situation: all real numbers at most 95 or at least 55?

To express the situation where all real numbers are at most 95 or at least 55, we can break this down into two parts:

• The phrase “at most 95” translates to the inequality: x ≤ 95.
• The phrase “at least 55” translates to the inequality: x ≥ 55.

Since these two conditions describe two separate ranges of values, we can combine them using the logical operator ‘or’. Therefore, we can write the compound inequality as:

x ≤ 95  x ≥ 55

This means that any real number x that is either less than or equal to 95 or greater than or equal to 55 satisfies the condition described.