The solution to 3x-x^2>2 is 1<x<2

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3x-x^2>2

Solution

3 x - x^{2} > 2

1 < x < 2

Interval Notation

(1, 2)

Solution steps

3 x - x^{2} > 2

Rewrite in standard form

3 x - x^{2} - 2 > 0

Factor

3 x - x^{2} - 2 : - (x - 1) (x - 2)

- (x - 1) (x - 2) > 0

Multiply both sides by

- 1

(reverse the inequality)

(- (x - 1) (x - 2)) (- 1) < 0 \cdot (- 1)

Simplify

(x - 1) (x - 2) < 0

Identify the intervals

1 < x < 2

- 13 x^{2} + 7.68 x + 0.4608 = 0

- 16 - - 9

3 x^{2} - 2 > 0

\frac{2}{x + 2} \geq \frac{1}{x - 1}

lo g_{2} (\frac{1}{32}) = - 5