The equation |$2x-5$| = 9 has two roots. How far apart are they on the number line?

A modulus equal to 9 means the expression inside is 9 or −9. From $2x-5=9$ we get $x=7$, and from $2x-5=-9$ we get $x=-2$. The gap between them is $7-(-2)=9$. (Missing the negative case leaves only the root 7.)