Answer
a. after year 2020.
b. after year 2024.
c. after year 2024.
d. after year 2020.
Work Step by Step
a. Given $I=\frac{x}{4}+26$, let $I\gt34$, we have $\frac{x}{4}+26\gt34$, $\frac{x}{4}\gt8$ and $x\gt32$, which corresponds to year $1988+32=2020$; that is, after year 2020.
b. Given $N=\frac{x}{4}+6$, let $N\gt15$; we have $\frac{x}{4}+6\gt15$, $\frac{x}{4}\gt9$ and $x\gt36$, which corresponds to year $1988+36=2024$; that is, after year 2024.
c. Find the intersection of the results from parts (a) and (b); we have $x\gt36$, or after year 2024.
d. Find the union of the results from parts (a) and (b); we have $x\gt32$, or after year 2020.
