what is the solution, if any, to the inequality 3 - |4 - n| > 1?\nno solution\nall real numbers\nn > 2 or n…

Explanation:

Step1: Isolate the absolute - value term

Subtract 3 from both sides of the inequality $3-\vert4 - n\vert>12$. $-\vert4 - n\vert>12 - 3$ $-\vert4 - n\vert>9$ Multiply both sides by - 1 and reverse the inequality sign. We get $\vert4 - n\vert<-9$.

Step2: Analyze the absolute - value property

The absolute - value of any real number $x$, denoted as $\vert x\vert$, is always non - negative, i.e., $\vert x\vert\geq0$ for all real numbers $x$. Since $\vert4 - n\vert$ is non - negative and we have the inequality $\vert4 - n\vert<-9$ (where the right - hand side is negative), there are no real numbers $n$ that satisfy this inequality.

Answer:

no solution