What is ((3x+4))/((5x+3))<((x+2))/((2x+3)) ?

The solution to ((3x+4))/((5x+3))<((x+2))/((2x+3)) is -3/2 <x<-3/5

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((3x+4))/((5x+3))<((x+2))/((2x+3))

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

- \frac{3}{2} < x < - \frac{3}{5}

Interval Notation

(- \frac{3}{2}, - \frac{3}{5})

Decimal Notation

- 1.5 < x < - 0.6

Solution steps

\frac{3 x + 4}{5 x + 3} < \frac{x + 2}{2 x + 3}

Rewrite in standard form

\frac{x ^{2} + 4 x + 6}{( 5 x + 3 ) ( 2 x + 3 )} < 0

Identify the intervals

- \frac{3}{2} < x < - \frac{3}{5}

x^{2} + 3 < 7

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

2 t^{2} - 7 t + 6 < 0

\frac{x}{( x - 2 )} - \frac{1}{( x + 3 )} > 0

(\frac{1}{4}) x \cdot (\frac{8}{3}) x \leq \frac{8}{27}

What is ((3x+4))/((5x+3))<((x+2))/((2x+3)) ?
The solution to ((3x+4))/((5x+3))<((x+2))/((2x+3)) is -3/2 <x<-3/5