The solution to x+11>10x^2 is -1<x< 11/10

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x+11>10x^2

Solution

x + 11 > 10 x^{2}

- 1 < x < \frac{11}{10}

Interval Notation

(- 1, \frac{11}{10})

Decimal Notation

- 1 < x < 1.1

Solution steps

x + 11 > 10 x^{2}

Rewrite in standard form

x + 11 - 10 x^{2} > 0

Factor

x + 11 - 10 x^{2} : - (x + 1) (10 x - 11)

- (x + 1) (10 x - 11) > 0

Multiply both sides by

- 1

(reverse the inequality)

(- (x + 1) (10 x - 11)) (- 1) < 0 \cdot (- 1)

Simplify

(x + 1) (10 x - 11) < 0

Identify the intervals

- 1 < x < \frac{11}{10}

x^{2} + 21 = 10 x - 3

(7 v)^{2}

3 c - 9 d + 7 c + 5 d

6 + 7 x - 3 x = 9 + 6

- \frac{x}{6} < - 6