SOLUTION: Explain why the equation |x| > -1/2 has all real number solutions.
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Question 1207731: Explain why the equation |x| > -1/2 has all real number solutions.
Found 2 solutions by ikleyn, math_tutor2020:
Answer by ikleyn(52787) (Show Source): You can put this solution on YOUR website!
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Explain why the equation |x| > -1/2 has all real number solutions.
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Left side is always positive or zero;
right side is negative.
All positive real numbers or zero is/are greater than any negative number.
Therefore, this inequality is valid for all real numbers x.
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Solved in full and explained completely.
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Comment from student: So, can we generally say that |expression| > negative number is always valid for all real numbers x?
My response: Yes, it is true.
Answer by math_tutor2020(3817) (Show Source): You can put this solution on YOUR website!
x is some real number on a number line
|x| represents the distance x is from 0.
Examples
|x| = |-27| = 27, showing x = -27 is 27 units away from 0.
|x| = |4| = 4, showing x = 4 is 4 units away from 0.
The output of |x| is never negative since negative distance isn't possible.
This ensures that |x| is larger than any negative number you can think of.
Therefore |x| > -1/2 is true for any real number x.
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