Question: Solve the following inequality. Graph the solution set.
|4x| \geq -7
Part 1 of 2
Select the correct choice and, if necessary, fill in the answer box to complete your choice.
A.
The solution set is { }.
(Type an integer or a simplified fraction. Use a comma to separate answers as needed.)
B.
The solution set is (\u221E,\u221E).
(Simplify your answer. Type your answer in interval notation. Use integers or fractions for any numbers in the expression)
C.
The solution set is the empty set.
1. **State the problem:** Solve the inequality $$|4x| \geq -7$$ and graph the solution set.
2. **Recall the property of absolute values:** The absolute value of any real number is always non-negative, i.e., $$|a| \geq 0$$ for any real number $$a$$.
3. **Analyze the inequality:** Since $$|4x|$$ is always $$\geq 0$$ and the right side is $$-7$$, which is negative, the inequality $$|4x| \geq -7$$ is always true for all real numbers $$x$$.
4. **Conclusion:** The solution set is all real numbers, which in interval notation is $$(-\infty, \infty)$$.
5. **Graphing:** The graph of the solution set is the entire real number line shaded.
**Final answer:** The solution set is $$(-\infty, \infty)$$.