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Popular >

x+1<6x^2

Solution

x + 1 < 6 x^{2}

Solution

x < - \frac{1}{3} or x > \frac{1}{2}

+2

Interval Notation

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

Decimal Notation

x < - 0.33333 \dots or x > 0.5

Solution steps

x + 1 < 6 x^{2}

Rewrite in standard form

x + 1 - 6 x^{2} < 0

Factor

x + 1 - 6 x^{2} : - (3 x + 1) (2 x - 1)

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

Multiply both sides by

- 1

(reverse the inequality)

(- (3 x + 1) (2 x - 1)) (- 1) > 0 \cdot (- 1)

Simplify

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

Identify the intervals

x < - \frac{1}{3} or x > \frac{1}{2}

Popular Examples

8 + 4 x = 2 x + 8 + 2 x

5 y^{2} - 4 = - y

simplify (y^6)/(y^4)simplify

\frac{y ^{6}}{y ^{4}}

- 2 < x \leq 1

5 ∣ 8 - x ∣ + 7 \leq 42

Frequently Asked Questions (FAQ)

What is x+1<6x^2 ?
The solution to x+1<6x^2 is x<-1/3 \lor x> 1/2