Answer: The answer to each question is as follows:
Will the border line be a solid or dotted line?
The border line will be a dotted line since the inequality is strict (y <).
Will the point (0, 0) be a part of the solution?
To determine if the point (0, 0) is part of the solution, we can substitute x = 0 and y = 0 into the inequality and see if it is true or false:
y < (-x+4)(x+1)/(x+1)
0 < (-(0)+4)(0+1)/(0+1)
0 < 4/1
0 < 4
Since 0 is less than 4, the inequality is true when x = 0 and y = 0. Therefore, the point (0, 0) is part of the solution.
Will the point (-1, 5) be a part of the solution?
To determine if the point (-1, 5) is part of the solution, we can substitute x = -1 and y = 5 into the inequality and see if it is true or false:
y < (-x+4)(x+1)/(x+1)
5 < (-(-1)+4)(-1+1)/(-1+1)
5 < 0/0
Since the denominator is 0, the inequality is undefined when x = -1 and y = 5. Therefore, we cannot say whether the point (-1, 5) is part of the solution or not.
What is the equation of the border line?
The inequality y < (-x+4)(x+1)/(x+1) can be rewritten as y < -x + 4. Therefore, the equation of the border line is y = -x + 4.
Explanation: