Question

Solve the inequalities and provide the solution steps for:

f(x) > 0
f(x) ≥ 0
f(x) < 0
f(x) ≤ 0
a) Step by step solution for all
b) Solutions for f(x) > 0 and f(x) < 0
c) Solutions for f(x) ≥ 0 and f(x) ≤ 0
d) No solution steps provided

Answer 1

To solve the inequalities f(x) > 0, f(x) ≥ 0, f(x) < 0, and f(x) ≤ 0 for the given function f(x), we can use step-by-step solutions and graphing calculators to determine the solutions. For f(x) > 0, the solution is 0 < x < 20, and for f(x) < 0, there are no values of x that satisfy the inequality.

Step-by-step explanation:

To solve inequalities, we first need to understand the symbols used. For greater than or less than inequalities, we use > and < symbols, respectively. For greater than or equal to or less than or equal to inequalities, we use ≥ and ≤ symbols.

Solution A:

1. For f(x) > 0, we look for the values of x that make f(x) greater than zero.
2. In this case, since the graph of f(x) is a horizontal line, f(x) will be greater than zero for all values of x between 0 and 20, exclusive (0 < x < 20).
3. The solution is 0 < x < 20.
4. For f(x) < 0, we look for the values of x that make f(x) less than zero.
5. Since the graph of f(x) is a horizontal line, f(x) will be less than zero for no values of x.
6. The solution is no values of x satisfy f(x) < 0.

Solution B:

For f(x) > 0, we can use a graphing calculator like the TI-83 or TI-84 to plot the graph of f(x) and identify the values of x that make f(x) greater than zero. The solution is 0 < x < 20.

For f(x) < 0, the graph of f(x) will never intersect the x-axis, indicating that there are no values of x that make f(x) less than zero. The solution is no values of x satisfy f(x) < 0.