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Popular >

(25)/x <x

Solution

\frac{25}{x} < x

Solution

- 5 < x < 0 or x > 5

+1

Interval Notation

(- 5, 0) \cup (5, \infty)

Solution steps

\frac{25}{x} < x

Rewrite in standard form

\frac{25 - x ^{2}}{x} < 0

Factor

\frac{25 - x ^{2}}{x} : \frac{- ( x + 5 ) ( x - 5 )}{x}

\frac{- ( x + 5 ) ( x - 5 )}{x} < 0

Multiply both sides by

- 1

(reverse the inequality)

\frac{( - ( x + 5 ) ( x - 5 ) ) ( - 1 )}{x} > 0 \cdot (- 1)

Simplify

\frac{( x + 5 ) ( x - 5 )}{x} > 0

Identify the intervals

- 5 < x < 0 or x > 5

Popular Examples

9 x = - 7

-1/4 (x-8)+1/2 (x+2)=x+3

- \frac{1}{4} (x - 8) + \frac{1}{2} (x + 2) = x + 3

(0.324-2x)^2*0.018=(0.0435+x)(0.0777+x)

(0.324 - 2 x)^{2} \cdot 0.018 = (0.0435 + x) (0.0777 + x)

∣ x + 8 ∣ = 1

15-6(2x-4)=8+2(5x-1)

15 - 6 (2 x - 4) = 8 + 2 (5 x - 1)

Frequently Asked Questions (FAQ)

What is (25)/x <x ?
The solution to (25)/x <x is -5<x<0\lor x>5