Ifx2≤16andx2>4, how many integral values of x are possible?a...
Given
To Find: Integral values of x that satisfy both the inequalities
Approach
- We will convert the inequality x2≤16
into (x+a) (x-a) ≤ 0 form and the inequality x2>4
- 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