Modulus properties

Very Important

  • The modulus of x, |x| equals the maximum of x and –x
  • For any two real numbers 'a' and 'b', 

                                  |a|+|b| ≥ |a+b|
                                    |a|-|b| ≤ |a-b|                                 

                                   |a.b| = |a| |b|

  • If |x| ≤ k then the value of x lies between –k and k, or –k ≤ x ≤ k
  • If |x| ≥ k then x ≥ k or x ≤ -k
  • For any real number 'a', $$a^2$$ = $$|a|^2$$

Formula Video


Question 1

Given that $$x^{2} - 6x + 5 \leq 0$$, where $$x$$ is an integer. What is the probability that $$|x| \leq 3$$?

Question 2

For two real numbers x and y, which of the following is NOT always true?

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