Answer:
9 integers.
Step-by-step explanation:
We have been given an inequality [tex]3n^2-4\leq 44[/tex] and we are asked to find the solution set for our given inequality.
Let us solve our given inequality by adding 4 to both sides of our equation.
[tex]3n^2-4+4\leq 44+4[/tex]
[tex]3n^2\leq 48[/tex]
Upon dividing both sides of our equation by 3, we will get,
[tex]\frac{3n^2}{3}=\frac{48}{3}[/tex]
[tex]n^2\leq 16[/tex]
Taking square root of both sides of our equation we will get,
[tex]n\leq \pm 4[/tex]
[tex]-4\leq n\leq 4[/tex]
The solution set for our inequality is integers between -4 to 4 including -4 and 4 as : -4,-3,-2,-1,0,1,2,3,4.
Therefore, 9 integers will satisfy our given inequality.
