Posted by **Rinchan** on Sunday, October 20, 2013 at 8:57am.

Solve the inequality 12x^3 + 8x^2 <= 3x + 2. Justify your answer.

- advanced functions -
**Reiny**, Sunday, October 20, 2013 at 9:28am
12x^3 + 8x^2 ≤ 3x + 2

12x3 + 8x^2 - 3x - 2 ≤ 0

after some trial and errors where I tried

x = ±1, ±2, etc, I found

x = ±1/2 and x = -2/3 give me zero

12x3 + 8x^2 - 3x - 2 ≤ 0

(2x-1)(2x+1)(3x+2) ≤ 0

knowing the behaviour of

y = 12x3 + 8x^2 - 3x - 2

and having x-intercepts of -2/3, -1/2 and +1/2

the solution would be

x ≤ -2/3 OR -1/2 ≤ x ≤ 1/2

confirmation:

http://www.wolframalpha.com/input/?i=plot+12x3+%2B+8x%5E2+-+3x+-+2+≤+0

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