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Popular >

1/(x^2)<100

Solution

\frac{1}{x ^{2}} < 100

Solution

x < - \frac{1}{10} or x > \frac{1}{10}

+2

Interval Notation

(- \infty, - \frac{1}{10}) \cup (\frac{1}{10}, \infty)

Decimal Notation

x < - 0.1 or x > 0.1

Solution steps

\frac{1}{x ^{2}} < 100

Rewrite in standard form

\frac{1 - 100 x ^{2}}{x ^{2}} < 0

Factor

\frac{1 - 100 x ^{2}}{x ^{2}} : \frac{- ( 10 x + 1 ) ( 10 x - 1 )}{x ^{2}}

\frac{- ( 10 x + 1 ) ( 10 x - 1 )}{x ^{2}} < 0

Multiply both sides by

- 1

(reverse the inequality)

\frac{( - ( 10 x + 1 ) ( 10 x - 1 ) ) ( - 1 )}{x ^{2}} > 0 \cdot (- 1)

Simplify

\frac{( 10 x + 1 ) ( 10 x - 1 )}{x ^{2}} > 0

Identify the intervals

x < - \frac{1}{10} or x > \frac{1}{10}

Popular Examples

\frac{2}{5} x - \frac{1}{3} x = 2

- 1 \leq x \leq 1

∣ x - 4 ∣ < 5

simplify 5^{1/2}*5^{3/2}simplify

5^{\frac{1}{2}} \cdot 5^{\frac{3}{2}}

-4x^2+0.01x+0.0005=0

- 4 x^{2} + 0.01 x + 0.0005 = 0

Frequently Asked Questions (FAQ)

What is 1/(x^2)<100 ?
The solution to 1/(x^2)<100 is x<-1/10 \lor x> 1/10