Final answer:
To solve 'one-third of a number is at least 5 units from 31,' set up two inequalities representing 5 units more and 5 units less than 31, leading to x being at least 108 and also at least 78.
Step-by-step explanation:
The student's question asks us to solve an inequality that states 'one-third of a number is at least 5 units from 31'. To express this mathematically, we need to consider two scenarios: when one-third of the number is 5 units more than 31, and when it is 5 units less.
So we set up the inequalities 1/3x ≥ 31 + 5 and 1/3x ≥ 31 - 5. Simplifying these gives us x ≥ 108 and x ≥ 78. Therefore, x must be at least 108 to satisfy the first inequality and x must also be greater than or equal to 78 to satisfy the second inequality.