What is (1/4 b-1)/5 b> 3/10 b-1/2 ?

The solution to (1/4 b-1)/5 b> 3/10 b-1/2 is b sqrt(15)+5

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(1/4 b-1)/5 b> 3/10 b-1/2

\frac{\frac{1}{4} b - 1}{5} b > \frac{3}{10} b - \frac{1}{2}

b < - 15 + 5 or b > 15 + 5

Interval Notation

(- \infty, - 15 + 5) \cup (15 + 5, \infty)

Decimal Notation

b < 1.12701 \dots or b > 8.87298 \dots

Solution steps

\frac{\frac{1}{4} b - 1}{5} b > \frac{3}{10} b - \frac{1}{2}

Rewrite in standard form

b^{2} - 10 b + 10 > 0

Complete the square

b^{2} - 10 b + 10 : (b - 5)^{2} - 15

(b - 5)^{2} - 15 > 0

Move

15

to the right side

(b - 5)^{2} > 15

For

u^{n} > a

, if

n

is even then

b - 5 < - 15 or b - 5 > 15

b - 5 < - 15 : b < - 15 + 5

b - 5 > 15 : b > 15 + 5

Combine the intervals

b < - 15 + 5 or b > 15 + 5

∣ 3 d ∣ + 6 = 15

(8 a^{- 6})^{- \frac{2}{3}}

x^{2} - 2 x = 48

12.8 = \frac{x}{8}

2 x - 1 < 3 x + 2 < 14

What is (1/4 b-1)/5 b> 3/10 b-1/2 ?
The solution to (1/4 b-1)/5 b> 3/10 b-1/2 is b<-sqrt(15)+5\lor b>sqrt(15)+5