Question

Which number is a solution of the inequality?

Answer 1

we know that

A number is an inequality solution if the number satisfies the inequality

Part 1) $10.6 < b$

rewrite the inequality

$b > 10.6$

The answer Part 1) is the option D $14$

Because  $14$ satisfies the inequality

$14 > 10.6$ -----> is true

Part 2) $m > 7/12$

The answer Part 2) is the option A $1$

Because  $1$ satisfies the inequality

$1 > 7/12$ -----> is true

Part 3) $8< x(7-x)$

we're going to verify every case

case A) For $x=2$

substitute the value of x in the inequality

$8< 2(7-2)$

$8< 10$ ------> is true

therefore

The number $2$ is a solution

case B) For $x=8$

substitute the value of x in the inequality

$8< 8(7-8)$

$8< -8$ ------> is not true

therefore

The number $8$ is not a solution

case C) For $x=-1$

substitute the value of x in the inequality

$8< -1(7-(-1))$

$8< -8$ ------> is not true

therefore

The number $-1$ is not a solution

case D) For $x=0$

substitute the value of x in the inequality

$8< 0(7-0)$

$8< 0$ ------> is not true

therefore

The number $0$ is not a solution

therefore

The answer Part 3) is the option A $2$

Answer 2

Here are the answers of the given items above:
1.) 10.6 < b
The correct answer would be option D. 14. Among the given numbers, only 14 is greater than 10.6.
2. m>7/12
The correct answer would be option A. 1. 
3. 8 < x(7 - x)
The correct answer would be option A. 2
Here is the solution:
8 < 2(7 - 2)
8 < 2(5)
8 < 10
Hope this helps!