What is log_{10}(0.5)(x/((x+1)))<-1 ?

The solution to log_{10}(0.5)(x/((x+1)))<-1 is -1/(log_{10)(0.5)+1}<x<-1

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log_{10}(0.5)(x/((x+1)))<-1

lo g_{10} (0.5) (\frac{x}{( x + 1 )}) < - 1

- \frac{1}{lo g _{10} ( 0.5 ) + 1} < x < - 1

Interval Notation

(- \frac{1}{lo g _{10} ( 0.5 ) + 1}, - 1)

Decimal Notation

- 1.43067 \dots < x < - 1

Solution steps

lo g_{10} (0.5) \frac{x}{x + 1} < - 1

Rewrite in standard form

\frac{lo g _{10} ( 0.5 ) x + x + 1}{x + 1} < 0

Identify the intervals

- \frac{1}{lo g _{10} ( 0.5 ) + 1} < x < - 1

\frac{x}{( 4 x + 9 ) ( 3 - 7 x )} > 0

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

\frac{( 4 x + 3 )}{( 2 x - 5 )} < 6

\frac{( x - 4 )}{( 2 x - 3 )} < 3

x + 1 < \frac{6}{x}

What is log_{10}(0.5)(x/((x+1)))<-1 ?
The solution to log_{10}(0.5)(x/((x+1)))<-1 is -1/(log_{10)(0.5)+1}<x<-1