So I have this problem:

Question

Dave can vote. (18 or over.) Dave is 5 years older than Jim. Jim is not old enough to vote. Write a mathematical inequality expressing Dave's age. (Hint: determine Dave's maximum and minimum age.)

So I have his minimum age as 18 and his maximum age as 22. That's how old he can be while the other is too young to vote. But how do I write the inequality?

Answer 1

let J=Jim's age
let D=Dave's age
It is given that Dave can vote.
So
D>=18
Dave is 5 years older
J+5=D
or
J=D-5
Jim can't vote.
J<18
Substitute for Jim's age:
D-5<18
Solve this for the upper limit for Dave's age.