First of all, it might be convenient to rewrite the inequality as
[tex]26-x^2>4x-20 \iff x^2+4x-46<0[/tex]
Then, we can plug the proposed value to see which one satisfies the inequality: we want the expression to evaluate to a negative value.
x=8:
[tex]x^2+4x-46 \implies 64+32-46 = 50>0[/tex]
x=7
[tex]x^2+4x-46 \implies 49+28-46 = 31>0[/tex]
x=6
[tex]x^2+4x-46 \implies 36+24-46 = 14>0[/tex]
x=5
[tex]x^2+4x-46 \implies 25+20-46 = -1<0[/tex]
So, the only value that returns a negative value is x = 5.
