Determine which point is part of the solution

Saif Qureshi

Saif Qureshi

Answered question

2022-06-27

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.

Answer & Explanation

Mr Solver

Mr Solver

Skilled2023-05-25Added 147 answers

To determine which point is part of the solution set to the system of inequalities: f(x)<x+4, f(x)>x3, and f(x)<5, we need to evaluate each point and check if it satisfies all three inequalities.
Let's consider a point (x,y) and substitute its coordinates into each inequality to see if it holds true.
1. For f(x)<x+4, we substitute y into f(x):
y<x+4
2. For f(x)>x3, we substitute y into f(x):
y>x3
3. For f(x)<5, we substitute y into f(x):
y<5
Now, let's examine each point and see which one satisfies all three inequalities:
1. Point A: (2, 1)
Substituting the coordinates into the inequalities:
1<2+4
1>23
1<5
Point A satisfies all three inequalities.
2. Point B: (-3, 6)
Substituting the coordinates into the inequalities:
6<3+4not satisfied
6>33
6<5not satisfied
Point B does not satisfy the first and third inequalities.
3. Point C: (0, -1)
Substituting the coordinates into the inequalities:
1<0+4
1>03
1<5
Point C satisfies all three inequalities.
Based on the evaluations, the point (x,y)=(2,1) and (x,y)=(0,1) are part of the solution set to the given system of inequalities.

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