Question

How many integers n satisfy the inequality 3n² - 4≤44?

Answer 1

Answer:

The possible values of n  for n ≤ +4  =  (-∞,+4]

The possible values of n for  n ≤ -4  =  (-∞,-4]

Step-by-step explanation:

Here, the given inequality is:

$3n^2 - 4 \leq 44$

Firstly, let us solve the given inequality for the desirable value of n.

$3n^2 - 4 \leq 44$

Adding 4 on both sides, we get:

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

$3n^2 \leq 48$

or, $n^2 \leq \frac{48}{3}\implies n^2 \leq 16$

⇒   n ≤ +4  or  n ≤ -4

So, the possible values of n  for  n ≤ +4  =  (-∞,+4]

And,  the possible values of n  for  n ≤ -4  =  (-∞,-4]

So, we can pick any of the integer values from the both defined sets.