1. How many integers satisfy \($(n-2)(n+4)<0$\)?

2. Find all values of \($t$\)such that\($8t^2 \le 3-10t$\) .\($8t^2 \le 3-10t$\)

Guest Apr 5, 2017

#1**+1 **

(n - 2) ( n + 4) < 0 set equal to 0

(n - 2) ( n + 4) = 0

Setting both factors to 0 and solving for n we have that n = 2 and n = -4

And the possible solution intervals are (-inf, -4) , (-4, 2) or ( 2, inf)

And notice that the interval (-4, 2) is the one that solves the original inequality

8t^2 ≤ 3 - 10t rearrange as

8t^2 + 10t - 3 ≤ 0 (2) factor as

(4t - 1) (2t + 3) ≤ 0

Set both factors to 0 and solve or t and we have that t = 1/4 and t = -3/2

And the possible solution intervals are (-inf, -3/2) , (-3/2, 1/4 ) or ( 1/4, inf)

And notice that the interval (-3/2, 1/4) is the one that solves (2)

CPhill
Apr 5, 2017