To find elements of truth set

Question

STATEMENT : $x$ is a real number and $5$ $\in$ {$y$ is real number | $x^2+y^2 <50$ }.

Since $5$ is element of above set. so we have $x^2 + 25 < 50$. so we have $x^2 < 25$. So Truth set is {$-4,-3,-2,-1,0,1,2,3,4$}. Is my work correct? Thank you

Answer 1

You assumed $x$ is an integer. But $4.9$ is an allowed value for $x$.

$x^2<25$ is equivalent to $|x|<5$ or $x\in (-5,5).$