To determine which of the given x-value ranges indicates no movement of the object, we can analyze each option based on typical behaviors of object movement in a coordinate plane.
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\(-5 \le x \le 5\): This range includes all possible x-values from -5 to 5, indicating movement across the entire range.
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\(1 \le x \le 4\): This range is limited to just the x-values from 1 to 4, indicating that the object is moving in a confined segment of the plane.
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\(-2 \le x \le 1\): This range includes x-values from -2 to 1, also indicating that the object is moving in a segment of the plane.
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\(-5 \le x \le -2\): This range includes x-values from -5 to -2, indicating that the object is moving in that segment of the plane.
To indicate no movement, we would expect either a point or a range of x-values where the object does not change its position (i.e., there would be no range). However, since all the ranges given involve movement from one point to another, we need to think of it in terms of the "change in position."
Based on the information, the closest option indicating no movement would be a range that is as small as possible. However, since all options show ranges where movement occurs, if we had to select one that suggests a confined movement, we would select \(-5 \le x \le -2\) as it represents the largest span of negative movement but does not necessarily indicate no movement.
If the goal is strictly to find the "no movement" range, none of the given options accurately reflects that, as they all represent movement in different segments of the plane. However, if we need to choose one based on limiting movement, the response should be \(-5 \le x \le -2\) as it does not go beyond -2 (indicating being confined to a smaller range, which could suggest stationary movement rather than active movement).
In conclusion, amongst the options provided, the response that would suggest the least movement might be \(-5 \le x \le -2\), as it indicates confinement to a limited range.