Final answer:
To solve the inequalities, one must isolate x and possibly use the quadratic formula if the inequality is of quadratic nature.
Step-by-step explanation:
The question relates to solving inequalities, which can also involve quadratic equations. When solving inequalities like −4x + 60 < 72 or 14x + 11 < −31, it's important to isolate x on one side of the inequality.
For the first inequality, subtract 60 from both sides:
−4x < 12 ⇒ x > −3 (since dividing by a negative number reverses the inequality sign).
For the second inequality, subtract 11 from both sides and then divide by 14:
14x < −42 ⇒ x < −3.
When dealing with quadratic formulas, the general form of a quadratic equation is at² + bt + c = 0, where a, b, and c are constants. The solutions are found using the quadratic formula:
x = −b ± √(b² − 4ac) / (2a).
It's important to evaluate both positive and negative solutions, but in some real-life contexts, a negative solution may not make sense and can be discarded.