To solve the inequality [tex]\( |2x + 5| \geq -7 \)[/tex], let's carefully analyze and go through the steps:
1. Understanding Absolute Values:
- The absolute value of any real number is always non-negative. This means [tex]\( |2x + 5| \)[/tex] is always greater than or equal to 0.
2. Compare with the Right-Hand Side:
- The inequality given is [tex]\( |2x + 5| \geq -7 \)[/tex].
- Since [tex]\( |2x + 5| \)[/tex] is always non-negative and therefore always greater than or equal to 0, it will always be greater than or equal to [tex]\(-7\)[/tex].
3. Conclusion:
- Given that [tex]\( |2x + 5| \geq -7 \)[/tex] is always true because [tex]\( |2x + 5| \)[/tex] is always at least 0, the solution to the inequality is all real numbers.
To summarize, the inequality [tex]\( |2x + 5| \geq -7 \)[/tex] is always true for any real number [tex]\( x \)[/tex].
Graphing the Solution:
- Since the solution includes all real numbers, you would represent this on a number line by shading the entire line, indicating that every point on the line (every real number) is a solution.
The step-by-step solution shows the understanding that the absolute value is non-negative and hence the inequality holds for all real numbers. Thus, the graph of the solution on a number line would be a fully shaded line covering all real numbers.
