I use command Reduce
to solve an inequality. First, I used
Reduce[Sqrt[4 x + 5] - Sqrt[-6 x + 10] <= Sqrt[2 x - 1], x]
and got
x < -(5/4) || 1/2 <= x <= 1
I put
f[x_] := Sqrt[4 x + 5] - Sqrt[-6 x + 10] - Sqrt[2 x - 1]
and found $f[-2]$,
I Sqrt[3] - I Sqrt[5] - Sqrt[22]
That is meant I Sqrt[3] - I Sqrt[5] - Sqrt[22]<= 0
. I think, this is wrong.
Second, I used
Reduce[Sqrt[4 x + 5] - Sqrt[-6 x + 10] <= Sqrt[2 x - 1], x, Reals]
I got
1/2 <= x <= 1
Is this a bug with Reduce[Sqrt[4 x + 5] - Sqrt[-6 x + 10] <= Sqrt[2 x - 1], x]
?