Please help with this A-level question, after days I still have no idea how to reach the correct answer

Question

Questions on Quadratic Inequalities:

Solve the following inequalities, giving your answers in set notation:

1. −x² > 4x ² − 5

The answer I've been told is correct is, {x:x > −5} ∩ {x:x < 1}, However I have no idea how they got this answer as the only answer that makes sense to me is {x:x > −1} ∩ {x:x < 1}.

Answer 1

add x^2 to both sides, also add 5 to both sides to get

5>5x^2, now divide by 5

1> x^2

x^2<1

two ways x^2 < 1

take the square root of both sides to get x<1 and x>-1 simultaneously

-1<x < 1

that's the same as the answer you have, with an intersection of x<1 and x>-1

to see that maybe try a few simple integers in that interval and outside

x=0. x^2 = 0^2 = 0 <1

x=2 x^2 =2^2 = 4 which is not < 1

x=-2 x^2 = (-2)^2 = 4 which is also not <1

the absolute value of x has to be less than 1, which means x<1 and -x<1. -x<1 is equivalent to x>-1. Multiply by -1 reverses the inequality from < to >