Which solution to the given inequality is correct?

Question

If the inequality is given as

$$b_1^2b_2-b_2K_1M_1-K_1M_1(b_2+B)\leq 0$$

where $b_1 = b_2 = 1$, $K_1=10$, and $M_1 = 2$

then solution number 1:

$$1-20-20-20B \leq 0$$

$$-20B \leq 39$$

$$B \leq -\frac{39}{20}$$

the solution number 2:

$$1-20-20-20B \leq 0$$

$$-39-20B \leq 0$$

$$-39 \leq 20B$$

$$B\geq -\frac{39}{20}$$

Answer 1

The inequality should actually be $1- 20-20-20(1+B)\le0$

$1-60-20B\le0$

$20B\ge-59$

$\implies B\ge\dfrac{-59}{20}$

Answer 2

In your first solution <= should be changed to => when you do -20B<= 39.