To determine the solution to the inequality [tex]\( |x| - 2 \leq -3 \)[/tex], let's go through the steps:
1. We start with the inequality:
[tex]\[
|x| - 2 \leq -3
\][/tex]
2. Add 2 to both sides of the inequality to isolate the absolute value term:
[tex]\[
|x| - 2 + 2 \leq -3 + 2
\][/tex]
Simplifying this, we get:
[tex]\[
|x| \leq -1
\][/tex]
3. Now, we consider the property of absolute value. The absolute value [tex]\( |x| \)[/tex] of any real number [tex]\( x \)[/tex] is always non-negative, meaning [tex]\( |x| \)[/tex] is always greater than or equal to 0. Therefore, the inequality [tex]\( |x| \leq -1 \)[/tex] suggests that [tex]\( |x| \)[/tex] should be less than or equal to a negative number, which is impossible because absolute values are never negative.
Based on this reasoning, there is no real number [tex]\( x \)[/tex] that can satisfy the inequality [tex]\( |x| \leq -1 \)[/tex].
Thus, the solution to the inequality is:
A. No solution
