Final answer:
To solve the inequality 84 < -13 - u, add 13 to both sides to get 97 < -u. Then multiply by -1, remembering to reverse the inequality sign, resulting in u < -97.
Step-by-step explanation:
The student has presented an inequality 84 < -13 - u.
To solve for u, we need to isolate it on one side of the inequality.
First, we subtract -13 from both sides to maintain the equality, as per the property explained in LibreTexts™.
The inequality becomes 84 + 13 < -u, which simplifies to 97 < -u.
Next, we multiply both sides of the inequality by -1 to solve for u, and since multiplying or dividing both sides of an inequality by a negative number reverses the inequality sign, we get -97 > u.
Therefore, the solution to the inequality is u < -97.