Given (x+2)/(m) + (3x+3)/(k) = (15x+24)/(18), find the value of k. Show your working clearly.

The three lines are given as:

1. $y = -2x + 12$
2. $y = 2x + 4$
3. $y = -0.5x + 4$

For the line $y = -2x + 12$: The shaded region is below this line. This means the y-values in the shaded region are less than or equal to the y-values on the line.
So, the inequality is $y \le -2x + 12$.

For the line $y = 2x + 4$: The shaded region is below this line. This means the y-values in the shaded region are less than or equal to the y-values on the line.
So, the inequality is $y \le 2x + 4$.

For the line $y = -0.5x + 4$: The shaded region is above this line. This means the y-values in the shaded region are greater than or equal to the y-values on the line.
So, the inequality is $y \ge -0.5x + 4$.

The three inequalities that satisfy the region R are:

$$y \le -2x + 12$$ $$y \le 2x + 4$$ $$y \ge -0.5x + 4$$

The three inequalities which satisfy the region R are:

$$\boxed{y \le -2x + 12}$$ $$\boxed{y \le 2x + 4}$$ $$\boxed{y \ge -0.5x + 4}$$