Explanation:
We need to find the number of integral values of x satisfying the inequality √(−x^2+10x−16) < x="" −="" />

Step 1: Simplify the inequality
We start by squaring both sides of the inequality to eliminate the square root:

−x^2+10x−16 < (x="" −="" />
−x^2+10x−16 < x^2="" −="" 4x="" +="" />
2x^2 − 14x + 20 > 0
x^2 − 7x + 10 > 0
(x − 5)(x − 2) > 0

Step 2: Solve for x
The inequality (x − 5)(x − 2) > 0 is true when x < 2="" or="" x="" /> 5. We can represent this solution set on a number line as:

<---o---o---o---o---o--->
-1 0 1 2 3 4 5 6 7

The solution set is the set of x values that are less than 2 or greater than 5. This includes all integers less than 2 and greater than 5.

Step 3: Count the number of integral solutions
The integers less than 2 are −1, −2, −3, and −4. The integers greater than 5 are 6 and 7. Therefore, the number of integral solutions is 6 (−4, −3, −2, −1, 6, and 7).

Final answer:
There are 6 integral values of x satisfying the inequality √(−x^2+10x−16) < x="" −="" 2.="" x="" −="" />