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

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-3x^2>2x-1

Solution

- 3 x^{2} > 2 x - 1

- 1 < x < \frac{1}{3}

Interval Notation

(- 1, \frac{1}{3})

Decimal Notation

- 1 < x < 0.33333 \dots

Solution steps

- 3 x^{2} > 2 x - 1

Rewrite in standard form

- 3 x^{2} + 1 - 2 x > 0

Factor

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

- (3 x - 1) (x + 1) > 0

Multiply both sides by

- 1

(reverse the inequality)

(- (3 x - 1) (x + 1)) (- 1) < 0 \cdot (- 1)

Simplify

(3 x - 1) (x + 1) < 0

Identify the intervals

- 1 < x < \frac{1}{3}

\frac{a ^{4}}{a ^{2}}

64 a^{3} + 125

\frac{5}{2} + \frac{3}{8}

2 ab - 3 b c

4 + \frac{k}{2} > 8