Question

For each of the given statements:

[b ,if , x = |x|]
a) (x ≥ 0)
b) (x ≤ 0)
c) (x ≥ 1)
d) (x ≤ 1)

Answer 1

The statement 'x = |x|' indicates that x is non-negative. Sub-statements (a) 'x ≥ 0' is true while (b), (c), and (d) are false as they incorrectly confine the values x can take, given the definition of the absolute value.

Step-by-step explanation:

The equation x = |x| implies that x must be non-negative because the absolute value of any number is always positive or zero. Therefore, let's assess the truth value of the following statements:

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• (a) x ≥ 0 - True, since by definition the absolute value |x| is always greater than or equal to zero.
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• (b) x ≤ 0 - False, because if x were less than zero, it would not be equal to its absolute value |x|. The correct statement is x ≥ 0.
• 
  
• (c) x ≥ 1 - False, as |x| can be equal to numbers less than one as well, including zero. The correct statement would not exclude values between zero and one, so there is no single 'correct statement' for this as it lies outside the scope of the initial equation.
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• (d) x ≤ 1 - False, |x| can also be larger than one. There is again no single 'correct' version because the absolute value |x| can be any non-negative number, not limited to those less than or equal to one.