Question

How many integers $n$ satisfy the inequality $3n^2 - 4 \le 44$

Answer 1

$\textbf{Given:}$

$3n^2-4\leq\;44$

$\text{Add 4 on both the sides of the inequality}$

$3n^2\leq\;48$

$\text{Divide 3 on both the sides of the inequality}$

$n^2\leq\;16$

$n^2-16\leq\;0$

$(n-4)(n+4)\leq\;0$

$\implies\;n\in\;[-4,4]$

$\text{since n is an integer, we have}$

$n=-4,-3,-2,-1,0,1,2,3,4$

$\therefore\textbf{There are 9 integers satisfying the given condition}$

Answer 2

9 integers $n$ satisfy the inequality $3n^2 - 4 \le 44$

• Given,

• 3n^2 - 4 < 44

• 3n^2 < 44 + 4

• 3n^2 < 48

• n^2 < 16

• n < +/- 4

• ∴ n ∈ [ -4, 4 ]

• we have n = -4 to 4, a total of 9 integers.

• -4, -3, -2, -1, 0, 1, 2, 3, 4