Question

Which value of x makes the open sentence true?

Answer 1

First of all, it might be convenient to rewrite the inequality as

$26-x^2>4x-20 \iff x^2+4x-46$

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:

$x^2+4x-46 \implies 64+32-46 = 50>0$

x=7

$x^2+4x-46 \implies 49+28-46 = 31>0$

x=6

$x^2+4x-46 \implies 36+24-46 = 14>0$

x=5

$x^2+4x-46 \implies 25+20-46 = -1$

So, the only value that returns a negative value is x = 5.

Answer 2

I hope it helps you get it right