What is 12x^3+8x^2<= 3x+2 ?

The solution to 12x^3+8x^2<= 3x+2 is x<=-2/3 \lor-1/2 <= x<= 1/2

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12x^3+8x^2<= 3x+2

12 x^{3} + 8 x^{2} \leq 3 x + 2

x \leq - \frac{2}{3} or - \frac{1}{2} \leq x \leq \frac{1}{2}

Interval Notation

(- \infty, - \frac{2}{3}] \cup [- \frac{1}{2}, \frac{1}{2}]

Decimal Notation

x \leq - 0.66666 \dots or - 0.5 \leq x \leq 0.5

Solution steps

12 x^{3} + 8 x^{2} \leq 3 x + 2

Rewrite in standard form

12 x^{3} + 8 x^{2} - 2 - 3 x \leq 0

Factor

12 x^{3} + 8 x^{2} - 2 - 3 x : (3 x + 2) (2 x + 1) (2 x - 1)

(3 x + 2) (2 x + 1) (2 x - 1) \leq 0

Identify the intervals

x \leq - \frac{2}{3} or - \frac{1}{2} \leq x \leq \frac{1}{2}

\frac{x + 1}{x - 1} > 0

x^{2} - 4 x - 21 > 0

\frac{x + 6}{x - 7} \leq 1

5 x^{2} + x^{3}

5 x^{2} - x - 4 = - 9 x

What is 12x^3+8x^2<= 3x+2 ?
The solution to 12x^3+8x^2<= 3x+2 is x<=-2/3 \lor-1/2 <= x<= 1/2