What is (x+1)/(10x+1)>= 1/(x+5) ?

The solution to (x+1)/(10x+1)>= 1/(x+5) is x -1/10

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(x+1)/(10x+1)>= 1/(x+5)

\frac{x + 1}{10 x + 1} \geq \frac{1}{x + 5}

x < - 5 or x > - \frac{1}{10}

Interval Notation

(- \infty, - 5) \cup (- \frac{1}{10}, \infty)

Decimal Notation

x < - 5 or x > - 0.1

Solution steps

\frac{x + 1}{10 x + 1} \geq \frac{1}{x + 5}

Rewrite in standard form

\frac{x ^{2} - 4 x + 4}{( x + 5 ) ( 10 x + 1 )} \geq 0

Factor

\frac{x ^{2} - 4 x + 4}{( x + 5 ) ( 10 x + 1 )} : \frac{( x - 2 ) ^{2}}{( x + 5 ) ( 10 x + 1 )}

\frac{( x - 2 ) ^{2}}{( x + 5 ) ( 10 x + 1 )} \geq 0

Identify the intervals

x < - 5 or x > - \frac{1}{10}

4 x + 1 = - 3

17 - 9

7 x^{2} - 343 = 0

lo g_{2} (4) + lo g_{2} (8)

10 n^{2} = 7 n - 5

What is (x+1)/(10x+1)>= 1/(x+5) ?
The solution to (x+1)/(10x+1)>= 1/(x+5) is x<-5\lor x>-1/10