Question

The reciprocal of a number decreased by the reciprocal of twice the number is greater than or equal to 2. Find the number(s) for what this’s true

Answer 1

The number ---- x
the reciprocal of the number --- 1/x

"The reciprocal of a number decreased by the reciprocal of twice the number"
---- 1/x - 1/(2x)

1/x - 1/(2x) ≥ 2
2/2x - 1/2x ≥ 2
1/x ≥ 2
1 ≥ 2x
2x ≤ 1
x ≤ 1/2

test:
let x = 1/4
reciprocal --- 4
twice the number --- 1/2
reciprocal of twice the number --- 2
4 - 2 ≥ 2, yes!

let x = 5
reciprocal --- 1/5
twice the number --- 10
reciprocal of twice the number --- 1/10
1/5 - 1/10 ≥ 2, no!, and that is what it should be