How can an inequality be manipulated to show a specific range of values?

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SUMMARY

The discussion focuses on the manipulation of the inequality -1 ≤ x ≤ 1 to derive the conclusion 0 ≤ x² ≤ 1. The key insight is recognizing that squaring any value within the interval [-1, 1] results in a non-negative value, specifically ranging from 0 to 1. The transformation from -1 to 0 occurs because squaring eliminates negative values, thus ensuring that x² is always non-negative within the specified range.

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  • Knowledge of interval notation
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shawli
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In an example in my textbook, it says the following:

"If -1 ≤ x ≤ 1, then 0 ≤ x2 ≤ 1. "


Can someone explain to me how to move from the first statement to the second statement please? I'm not quite sure how the -1 turned into a 0...
 
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Did you draw a graph of x^2 on the interval -1 ≤ x ≤ 1?
 
Ah right... it's staring me right in the face! So clear that I missed it haha. Thank you!
 

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