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If x2≤16andx2>4, how many integral values of x are possible?
  • a)
    0
  • b)
    1
  • c)
    3
  • d)
    4
  • e)
    6
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
Ifx2≤16andx2>4, how many integral values of x are possible?a...
Given
  • x2≤16  and x2>4
To Find: Integral values of x that satisfy both the inequalities
Approach
  1. We will convert the inequality x2≤16
 into (x+a) (x-a) ≤ 0 form and the inequality x2>4
  1.  into (x+b)(x-b) > 0 form and then draw the wavy line diagram to find out the integral values fo x that satisfy both the inequality.
Working Out
 
d. So, the inequality is true for range -4 ≤ x ≤ 4
e. Hence, the integral values of x in the range = {-4, -3, -2, -1, 0, 1, 2, 3, 4}
 
d. So, the inequality is true for range when x < -2 or x > 2
e. Hence, the integral values of x in the range = {-∞…….-4, -3, 3, 4, ………+∞}
 
3. The integral values of x that satisfy both the inequality are = { -4, -3, 3, 4}, i.e. 4 values.
 
Answer: D
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Ifx2≤16andx2>4, how many integral values of x are possible?a)0b)1c)3d)4e)6Correct answer is option 'D'. Can you explain this answer?
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