i need to prove that for every delta

i call d=delta

e=epsilon

1/|x+1|>e

we can choosr any e we want

so they took e=1/4

but because the innqualitty needs to work for every delta

they took x=min{2,(1+d)/2}

for d>2 it takes x= 1+d /2

for d<2 takes x=2

uppon what logic they found this formula x=min{2,(1+d)/2}