Find the smallest integer that satisfies the inequality (x-5)(x+5) < 0.

(x - 5) (x + 5)  < 0

x^2  - 25  < 0

Note that   (-5)   makes   (-5)^2 - 25  < 0    ⇒  25 - 25 < 0  ⇒  0 < 0  false

But

-4  makes   (-4)^2 - 25  < 0 ⇒   16 - 25 < 0  ⇒  -9 < 0    true

So...

x  = -4 is the smallest integer that makes this true

See this graph : https://www.desmos.com/calculator/6iwm6iiww6