Final answer:
To find a point that fits within the solution set of the given system of inequalities, you need to test each point against all three conditions. None of the provided points (0,0), (-6,0), (-3,4), or (4,6) satisfy all three inequalities of the system simultaneously. Therefore, none of the points are part of the solution set.
Step-by-step explanation:
To determine which point is part of the solution set to the following system of inequalities:
- f(x) < x + 4,
- f(x) > -x - 3, and
- f(x) < 5,
you need to evaluate each point to see if it satisfies all three inequalities. Here's a step-by-step explanation:
- Plug in the x-coordinate of each point into the inequalities.
- Check if the y-coordinate is less than x+4, greater than -x-3, and less than 5.
- If all three conditions are met, the point is part of the solution set.
Option C: (-3, 4) satisfies all three inequalities:
- 4 < (-3) + 4 is false,
- 4 > -(-3) - 3 is true,
- 4 < 5 is true.
Since one of the conditions is not met for option C, it is not part of the solution set.
After evaluating all options using the steps above, none of the provided points satisfies all three inequalities, so none of the points are part of the solution set.