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# Inequalities question

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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
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(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

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