A machined part must have a length within 0.05 millimeters of 20 millimeters to pass inspection. Which inequality describes the acceptable…

Being within $0.05$ millimeters of $20$ means the distance from $x$ to $20$ is at most $0.05$, which is written $|x-20|\le0.05$, choice F. This is the same as $19.95\le x\le20.05$. Choice J ($x\le20.05$) gives only the upper limit, so a part of length $5$ millimeters would pass. Choice G ($|x-0.05|\le20$) puts the numbers in the wrong places and describes lengths between $-19.95$ and $20.05$. Choice H ($|x+20|\le0.05$) is centered at $-20$. The form $|x-c|\le d$ describes values within $d$ of $c$.